Rare Variant Association Test for Common Complex Disease
- Objectives
- Introduction
- Rare Variant Association Analysis of Complex Diseases 2-1. Burden Test 2-2. Single nucleotide variant (SNV) Burden Test using EPACTS 2-3. Gene-based and Case-based Burden Test using EPACTS 2-4. SKAT association test 2-5. SKAT-O association test
- Linkage Disequilibrium Data Analysis 3-1. PED/MAP file formats 3-2. File format conversion from VCF to PED 3-3. Computation of Linkage Disequilibrium (between 2 genes?) 3-4. Visualizing the Linkage Disequilibrium w/ SNPplotter
- HLA alleles, HLA SNP, HLA amino acid, imputation (substituting for missing values)
0. Objectives
Although GWAS,which is based on the association study between single nucleotide variant and phenotypes, has been quite successful as a method of data analysis, could not explain quantitative complex traits (involving numerous plural genes). So the problem of “missing heritability” still remains in the complex disease area. So what’s missing heritability? It means that not all traits can be explained by SNPs detected picked up by GWAS and there may still be many heritable complex traits and complex diseases that have escaped detection and explained by interaction with the environment. These are some reasons that account for missing heritability:
Common SNPs not tagged well: a specific trait may not be explainable by common SNPs on a SNP array (they might just be tag SNPs, not actually causal SNPs). You would want SNPs that are near the gene of interest and consider haplotypes.
Rare variants: The trait is related to a rare variant. It’s not usually used as SNP array locus, so you can’t really figure it out with GWAS research. This requires determining sequencing the entire genome with NGS. And also requires understanding of large variant information systematically. You might think that checking out all the rare variants might solve the problem, but it’s not so. Explainability of common variant and rare variant in HGV2014 is about 50:50.
Other types of variants: There certainly are other types of variants other than SNPs. CNV or SV are like this. SV includes large structural change like translocation of chromosome.
Epistatis effects
Effects of Gene-Environment interaction
1. Introduction
Since mid 2000’s, there have been a lot of GWAS performed to figure out the characteristics of complex diseases and quantitative traits. GWAS is a technique to analyze common variants that occur with over 5% (MAFs). There have been over 2000 common variants related to diseases identified by GWAS. GWAS has elucidated associated genes in autophagy of Crohn’s disease, AMD (age-related macular degenration)‘s complementary pathway, etc., but has failed to explain many complex traits’ explanation. So 70 common variants found by GWAS and tracing-research of 150,000 could only explain about 11% of heritability of Type II diabetes. So generally about 80% of height’s heritability has been known, only about 4% of the heritability has been explained with about 40 associated genes discovered until 2009 via GWAS. Heritability itself is an incomplete measurement of correlation coefficient among family members, and therefore there has been some discussion that the 80% heritability is an overestimation. But it was still confounding that there was so much discrepancy between heritability estimated from family phenotype analysis versus GWAS-estimated heritability.
This sort of missing heritability issue became the que for focusing more on the research of low-frequency variants (5%\(\ge\)MAF$\(0.5%) and rare variants (0.5%\)$MAF). Rare variants are the cause of many Mendelian inherited diseases, and a great portion of Mendelian genetic disorders and rare subtypes of common disorders occur from rare variants with high penetrance. Evolutionarily speaking, deleterious variants that are disadvantageous to procreation get strong natural selection pressures, and therefore it is evident that the frequency is quite low. Loss of Function (LoF) variant that causes a protein’s function to become defunct typically show extremely low frequency. It is a well-established fact that rare variants are the cause of rare genetic disorders, but there are also numerous evidences that rare variants are also involved in common-complex disease etiology.
GWAs based on SNP assumes CDCV (Common Disease, Common Variant) hypothesis. Just as we assume that the cause of rare Mendelian diseases are usually associated with RDRVs (Rare Disease, Rare Variant), common diseases like diabetes or hypertension are supposed to be caused by common variants. This is the view that even complex diseases can be explained as combinations and interactinos among several to tens of common variants that occur at a rate of over 1-5%. For example, type II diabetes research published in Europe and Japan in 2010 respectively claimed that there are 12 and 2 markers repectively as variants that are associated with diabetic sensitivity/susceptibility. However, GWAS efforts to find associated markers with common-complex diseases have so far been quite futile and there’s still the issue of missing heritabiltiy problem. Now there’s a new alternative to these hypotheses called CDRV (Common Disease, Rare Variant) that says that even common traits and common diseases can be explained through combination of deleterious rare variants.
SNP chip, the experimental method at the core of GWAS, has its limitations in that our understanding and knowledge of rare variants are still incomplete and SNP chips are able to contain common variants, but not all the rare variants (just not physically feasible). On the other hand, NGS can analyze all the rare variants read by read. It will be a contest to be decided soon. However, even if we sequence all the variants, detection of disease-causing variants is not an easy problem. There’s also a problem of NGS cost (pretty high), but also the problem of low statistical power of current single-nucleotide focused asosciation study analytical method is still low unless there’s a promise of enough sample size or effect size.
In order to increase the low statistical power, RVAT (Rare Variant Association Test) methods to analyze the accumulated effect of a group of variants clustered together in a region to the complex trait/disease have been developed. Rare variant association study chooses the strategy that combines statistical frequency distribution, the accumulative effects of such, with intuitive effects of biological explainability. Burden test is a testing method that simplifies all the rare variants’ information in a region as one variable to perform association study with the phenotype of interest. There are subtypes like CMC, CAST, WST, etc. However, if there are (1) variants that have opposite correlations included in the region or (2) much of the variants do not have a causal relationship, the statistical power may become pretty weak. There are rare variant asosciation study methods other than as described in the table below:
2. Association Study of Rare variants in Complex Diseases
GWAS mainly focuses on SNPs that are common variants, so it has limitations that if the frequency of causal variants are low, it has much probability of failure. Rare variants are literally “rare” and it’s hard to gather enough number of samples for enough statistical power. Therefore we use the approach of grouping several to many rare variants in a gene or a locus (region) for association study with rare variants.
2-1. Burden Test
Burden test tests for how well the number of rare variants in a region or gene of interst explains its dependent variable like disease existence. For exapmle, we can find a gene or specific region that shows significant difference between case and control (diseased and normal) with increasing number of rare variants. Basically, we integrate (collapse) the information of all rare variants within that region into one variable (express how many number of variants are there and their orientation among themselves, etc.) and perform an association study with phenotypes. This enables biological interpretation of rare variants as a collapsed unit, which could not be discovered previously because of insufficient statistical power.
Next code shows clinical and variant data structure of seqMetaExample data, which is provided by seMeta library.
Install seqMeta.
Since seqMeta is no longer available in CRAN, I gotta install the archived version.
library(seqMeta)## Loading required package: survivaldata(seqMetaExample)head(Z1)## 1001797 1000452 1001692 1000219 1000679 1001623 1001799 1001243 1001421
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## 1000039 1000067 1001090 1000517 1001897 1000313 1000061 1001472 1000498
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## 1001724 1000308 1000737 1000558 1000109 1001571 1001670 1000310 1000826
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## 1000269 1001150 1001037 1000280 1001507 1001710 1001148 1001288 1001596
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## 1000965 1001321 1001084 1000725 1001107 1000823 1001774 1001995 1000528
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## 1000336 1001169 1001872 1000327 1000020 1000060 1000448 1001767 1000289
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## 1001118 1001259 1000068 1000229 1000889 1001307 1000101 1000076 1001129
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## 1001965 1001723 1001967 1000410 1001651 1000296 1000400 1000405 1001920
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## 1000969 1001626 1000787 1000412 1000282 1000671 1001336 1000324 1001616
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## 1000471 1001680 1001294 1001814 1000235 1001149 1001979 1001112 1000162
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## 1000932 1000489 1000276 1000901 1000891 1000343 1001271 1000140 1000730
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## 1000226 1001382 1001836 1001366 1000018 1000790 1001595 1000041 1001342
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## 1000496 1001615 1000104 1000420 1000581 1000357 1000559 1000251 1000433
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## 1001302 1001383 1000779 1001376 1000288 1001734 1001781 1001539 1000897
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## 1000842 1000363 1001800 1001127 1000645 1001543 1000163 1000977 1001216
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## 1000648 1001603 1000262 1000912 1000094 1001002 1001972 1001630 1000925
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## 1001119 1000013 1001950 1001250 1001134 1001981 1001214 1001708 1001687
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## 1001731 1001168 1001310 1002049 1001027 1000604 1001402 1001968 1000530
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## 1001387 1001811 1001520 1000562 1000064 1001014 1001349 1000493 1000066
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## 1000190 1001179 1001688 1000464 1000814 1001553 1000948 1000165 1001197
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## 1000756 1000960 1001144 1001282 1000599 1001815 1000395 1001657 1001422
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## 1000845 1000014 1000560 1000957 1001719 1001081 1001758 1000935 1000909
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## 1000797 1001587 1000612 1000680 1000991 1001375 1001825 1002032 1001810
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## 1000450 1001012 1000869 1001959 1001036 1001283 1001128 1001671 1001523
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## 1001335 1001956 1000027 1000421 1000683 1000218 1000746 1000981 1000270
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## 1001446 1001361 1001451 1000413 1000936 1001095 1000082 1000593 1001133
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## 1001381 1000441 1001736 1000649 1000818 1001136 1001556 1001181 1000467
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## 1001911 1001291 1000044 1001018 1001304 1001368 1000369 1000036 1001239
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## 1000987 1001114 1001510 1001406 1000442 1001338 1000996 1001498 1000580
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## 1001163 1001546 1001143 1000785 1000853 1000261 1001423 1001088 1000750
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## 1001869 1000775 1000539 1000470 1001255 1000716 1000576 1000682 1001418
## [1,] 0 0 0 0 0 0 0 0 0
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## 1000910 1001786 1001474 1000742 1001554 1001511 1000246 1001551 1001263
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## 1001743 1001899 1000543 1001062 1000455 1000142 1000417 1001934 1001108
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001374 1001768 1000632 1001171 1000706 1001862 1000253 1001471 1000856
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## 1000841 1000473 1001362 1001186 1001796 1000187 1001332 1000200 1001392
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 0 0 0 0 0 0 0 1
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## 1000279 1000938 1001681 1001557 1000616 1000603 1001750 1000908 1001727
## [1,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 1 0 0 0 0 0 0 0
## 1001326 1001519 1001669 1001515 1001823 1000993 1001715 1000962 1001827
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## 1000010 1000963 1001606 1000866 1000739 1001663 1000907 1001891 1000177
## [1,] 0 0 0 0 0 0 0 0 0
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## 1000375 1001195 1001884 1000659 1001135 1001247 1000660 1000942 1000393
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## 1001806 1001954 1000567 1001780 1000302 1001890 1000147 1001559 1000366
## [1,] 0 0 0 0 0 0 0 0 1
## [2,] 0 0 0 0 0 0 0 0 0
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## 1001305 1001060 1000967 1000457 1000516 1001042 1001788 1001311 1001749
## [1,] 0 1 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001916 1001678 1000015 1000624 1001280 1000930 1000721 1001296 1000795
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## 1001345 1000356 1001881 1001728 1000148 1001411 1000255 1001490 1000515
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## [2,] 1 0 0 0 0 0 0 0 1
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## 1000419 1000755 1001717 1000662 1001777 1000170 1001835 1000956 1001931
## [1,] 0 0 0 0 0 1 0 0 0
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## [3,] 0 0 0 0 0 0 2 0 0
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## 1001805 1000793 1001666 1000874 1001695 1000595 1000709 1001649 1000449
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## [2,] 0 1 0 0 0 0 0 0 0
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## 1002033 1000569 1000227 1001092 1000690 1000927 1000653 1000237 1000883
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001988 1001980 1000263 1002037 1001415 1002038 1000865 1001667 1001818
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## 1000547 1000946 1001725 1000301 1000208 1000902 1000670 1000361 1001839
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 1 0 0 0 0 0 1 0
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## 1001497 1001789 1001945 1000840 1001766 1001686 1000929 1000123 1000005
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## 1000974 1001629 1001654 1001922 1001203 1001918 1000122 1001096 1001033
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## 1001970 1001323 1000331 1001738 1000408 1001405 1000378 1001053 1001675
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## 1000748 1000536 1000230 1000564 1000838 1001503 1001763 1001561 1000843
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## 1001139 1001958 1000445 1001077 1000440 1001880 1000579 1000829 1000761
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## 1001984 1000238 1000913 1001224 1000864 1000589 1000355 1000854 1000479
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## 1002027 1000752 1001879 1000385 1000390 1001245 1001828 1000986 1001610
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## 1000325 1001312 1001913 1002010 1000885 1000116 1001803 1000540 1000233
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## 1000691 1000340 1001809 1000353 1000583 1001908 1001683 1001888 1000808
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## 1001194 1000975 1001991 1001401 1001544 1001274 1001707 1001358 1000054
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## 1000994 1000625 1000259 1001933 1000007 1000623 1001160 1000875 1000664
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## 1001849 1000879 1000081 1000090 1000966 1000053 1001940 1001455 1000334
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## 1000876 1001588 1001517 1001429 1001824 1000115 1001529 1000729 1001790
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## 1000264 1000863 1000998 1001083 1000880 1000298 1000497 1001434 1000672
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## 1000249 1000638 1000112 1001378 1000092 1001480 1001494 1001165 1000728
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## 1001917 1001653 1001457 1000857 1000861 1000075 1001726 1001072 1001174
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## 1001207 1000677 1001262 1001645 1001363 1001103 1002041 1001209 1001668
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## 1000477 1001844 1000848 1001380 1001486 1000896 1001348 1001943 1001030
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## 1000971 1001187 1001069 1001079 1001769 1001895 1000047 1001581 1002017
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## 1001685 1001597 1001521 1001491 1001113 1001218 1000414 1001438 1000291
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## 1001894 1001977 1000726 1000151 1000438 1001327 1001044 1001419 1001566
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## 1000931 1001585 1001636 1001260 1000031 1001016 1000243 1000326 1000831
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## 1001860 1000074 1001864 1001152 1001620 1001514 1001319 1000505 1000240
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1001500 1001855 1001071 1001882 1000573 1001276 1001997 1001172 1000922
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## 1000242 1000091 1001125 1000565 1001005 1000114 1001109 1000816 1001679
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## [2,] 1 0 0 0 0 0 0 0 0
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## 1001912 1001236 1000636 1000265 1001223 1000095 1000422 1001658 1000278
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## 1001691 1000384 1001316 1000510 1001365 1001479 1000692 1000776 1000030
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 0 0 0 0 0 0 0 1
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## 1000934 1001887 1000654 1001505 1002019 1000437 1000754 1000232 1000630
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## 1001532 1001957 1000132 1001782 1001126 1001265 1001104 1000488 1001025
## [1,] 0 0 0 0 0 1 0 0 0
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## 1001351 1000656 1001325 1001778 1001488 1000819 1001640 1001955 1001355
## [1,] 0 0 1 1 0 0 1 0 0
## [2,] 0 0 0 1 0 0 0 0 0
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## 1000225 1001536 1000391 1000900 1000943 1001641 1001579 1000884 1000531
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## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 1 0 0 0 0 0 0 0 0
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## 1001509 1001704 1001696 1000783 1000096 1000217 1000684 1001416 1001329
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## 1000601 1000988 1000911 1001555 1001085 1001199 1002023 1000978 1000089
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 1 0 0 0 0 0 0
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## [5,] 0 1 0 0 0 0 0 0 0
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## 1001530 1001989 1001427 1000708 1001711 1000293 1000377 1001011 1001056
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## 1000149 1000284 1000899 1000715 1001226 1001035 1000499 1000045 1001240
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## 1001495 1000117 1001393 1000439 1000995 1000903 1000634 1000381 1000979
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## 1000738 1000078 1000703 1001886 1000520 1000524 1001369 1002018 1001285
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1000514 1000143 1000718 1000533 1001960 1001403 1000120 1000383 1000871
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## [2,] 0 0 0 1 0 0 0 0 0
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## 1000711 1000121 1000341 1000098 1000989 1000424 1000661 1001364 1002042
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1001227 1000839 1000667 1001436 1000704 1000215 1002046 1001605 1000968
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## 1001435 1000702 1001618 1000763 1001045 1000643 1001055 1001467 1001974
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1000778 1001924 1000618 1000949 1001215 1000627 1001522 1000236 1001061
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## 1000919 1000588 1001643 1000024 1000821 1000210 1001407 1001206 1000973
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1000185 1000063 1001396 1001851 1000049 1000770 1001524 1000810 1001873
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1001776 1000136 1000083 1000626 1000764 1002047 1000782 1001049 1001170
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## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1002003 1002014 1000402 1000055 1001054 1000367 1001512 1002050 1001547
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## 1001470 1000300 1001889 1000042 1000792 1000551 1000146 1001807 1000144
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 1 1 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000924 1002002
## [1,] 0 0
## [2,] 0 0
## [3,] 1 0
## [4,] 0 0
## [5,] 0 0
## [6,] 0 0head(Z2)## 1001562 1001362 1001488 1001115 1001465 1000803 1000542 1001438 1000519
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 1 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 1 0 0 0 0 0 0 0 0
## 1000275 1000661 1002003 1001247 1000478 1000958 1001050 1000874 1000970
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## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 1
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1001354 1001019 1000233 1001989 1000829 1001967 1000608 1001638 1000522
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## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 1 1
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## 1000495 1000015 1001471 1000422 1001828 1001474 1001761 1000527 1001609
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001185 1001639 1001653 1000264 1001491 1001088 1000296 1000036 1000336
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## 1000983 1001193 1000875 1001777 1001345 1001831 1001211 1000001 1001958
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
## [3,] 0 0 0 0 1 0 0 1 0
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## [5,] 0 0 1 0 0 0 0 0 0
## [6,] 1 0 0 0 0 0 0 0 0
## 1000244 1000081 1001662 1000346 1000288 1001527 1000704 1001421 1001161
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 0 1 1 0 0 0 0 0 0
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## [5,] 0 0 0 1 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000082 1001709 1000405 1000816 1001534 1000427 1001289 1000585 1000797
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## 1001599 1000459 1000698 1002037 1001036 1002030 1001720 1001523 1000031
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## [6,] 1 0 0 0 0 0 0 0 0
## 1000387 1000128 1000988 1000537 1000968 1001694 1000523 1001315 1000281
## [1,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000058 1001970 1001622 1001868 1000136 1000391 1001695 1001203 1000345
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001033 1001068 1001282 1000656 1001448 1000525 1001903 1000457 1000021
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## [2,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000945 1000411 1000666 1001644 1001990 1000292 1001439 1000256 1001208
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1000730 1000920 1000688 1000171 1001156 1001392 1001003 1001337 1000777
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001384 1000129 1000494 1001213 1001703 1001928 1000508 1001632 1000132
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 1 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001946 1001081 1001080 1000682 1000728 1000220 1000550 1001382 1001045
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 0 0 0 0 0 0 0 0
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## 1001204 1000179 1001199 1001357 1000750 1000407 1000813 1001667 1001025
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
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## [6,] 0 0 0 1 0 0 0 0 0
## 1000088 1000759 1001685 1001347 1001396 1001544 1001149 1001979 1000341
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0
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## 1001611 1001058 1001974 1000972 1000701 1001824 1000080 1000365 1000578
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000756 1001108 1001689 1000454 1001768 1000062 1001490 1001222 1000312
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 1 0 0 0
## 1000914 1001743 1001174 1001569 1000832 1001487 1001405 1000452 1000838
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
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## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000305 1001216 1000120 1000597 1001801 1000142 1001026 1001269 1000634
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 1 0 0 0 0 0 0 1
## [5,] 0 1 0 0 0 0 0 0 0
## [6,] 0 0 1 0 0 0 0 0 0
## 1000140 1000771 1000768 1000493 1000056 1002020 1000351 1000491 1001346
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 0 0 0 0 0 1
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000301 1000762 1000106 1001916 1000349 1001128 1001913 1000153 1001735
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## 1001848 1000989 1000512 1001079 1001752 1000004 1001957 1001316 1000811
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000823 1000208 1000044 1000317 1000723 1001286 1001187 1001450 1001256
## [1,] 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
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## 1000124 1000442 1001499 1001141 1001482 1000090 1001304 1001417 1001464
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001239 1001466 1000788 1000451 1001390 1001502 1000371 1001790 1001389
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## 1001971 1001960 1000524 1000262 1000245 1001403 1001000 1000927 1000774
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## 1000509 1001295 1001860 1001847 1001251 1000344 1001943 1001587 1000897
## [1,] 0 0 0 0 0 0 0 0 0
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## 1000017 1000406 1000455 1001706 1000839 1001041 1000113 1001517 1000923
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## 1001070 1001060 1000842 1001242 1000002 1000981 1000921 1000114 1001321
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## 1000828 1000640 1001671 1001355 1000936 1000942 1000748 1000289 1001836
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## 1001900 1001969 1000450 1001173 1001129 1000022 1000187 1000818 1000959
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## 1001296 1000883 1001596 1001437 1001525 1001332 1001883 1000567 1001651
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## 1001636 1000271 1001150 1000822 1000520 1001978 1001317 1001530 1000575
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## 1000854 1001177 1000877 1000214 1001423 1000861 1000486 1000516 1001803
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## 1001481 1000731 1001257 1001842 1001406 1000801 1001413 1000320 1001713
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## 1001578 1001434 1000173 1000064 1001376 1000419 1000907 1000721 1000089
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## 1000126 1000053 1001690 1001776 1000826 1001018 1000860 1000583 1001047
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## 1000190 1000526 1000680 1001751 1000073 1001939 1001770 1001287 1001531
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## 1000334 1000318 1001400 1001769 1001084 1000261 1001721 1000145 1000402
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## 1000735 1001859 1002049 1001505 1000582 1000779 1000394 1001116 1000484
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## 1001228 1000830 1000996 1000054 1001302 1001546 1001221 1000609 1000151
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## 1000889 1000979 1000555 1000163 1001941 1001494 1001509 1001563 1000513
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## 1001869 1001085 1000363 1001774 1001519 1000880 1001034 1001764 1001016
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## 1001444 1000540 1001243 1000781 1000333 1000581 1001132 1000018 1000497
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## 1002014 1001702 1001839 1000827 1000279 1000935 1000743 1001986 1000998
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## 1000749 1001273 1001160 1000995 1001275 1001731 1000293 1000711 1000228
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## 1000138 1001291 1000910 1000672 1001153 1000453 1001489 1000109 1001087
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## 1000029 1000302 1000700 1001972 1001201 1000568 1001331 1002048 1001147
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## 1001170 1001889 1000825 1000410 1001929 1001571 1000848 1001399 1000574
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## 1000274 1000416 1001233 1001057 1001294 1000408 1000204 1000393 1000206
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## 1001782 1001637 1000869 1001038 1000971 1000092 1001592 1001236 1001602
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## 1000388 1000804 1000819 1001549 1001608 1000241 1000099 1001547 1000904
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## 1000438 1000223 1000414 1001468 1001745 1000488 1001785 1001053 1000957
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## 1000319 1000941 1001298 1000722 1001307 1000792 1001113 1001140 1002040
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## 1001855 1000280 1000602 1000046 1000360 1000066 1001377 1001746 1000515
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## 1000845 1001951 1000710 1001553 1001031 1000990 1001152 1000953 1000708
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## 1001473 1001532 1001035 1001566 1000870 1000911 1000258 1001359 1001807
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## 1001843 1000501 1001705 1000100 1001579 1000906 1000890 1000934 1000439
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## 1000074 1001106 1000776 1001516 1000168 1001895 1001412 1000378 1000510
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## 1001136 1000020 1001458 1000409 1000865 1000447 1000461 1000699 1001191
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## 1000060 1000259 1001788 1001885 1000623 1000118 1001120 1001767 1000628
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## 1000306 1001078 1001520 1000744 1000932 1001197 1000853 1001395 1000919
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## 1000580 1000040 1001844 1000760 1000290 1000766 1001591 1000780 1000859
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## 1000645 1000487 1002009 1000596 1000903 1001894 1001849 1000636 1000131
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## 1001661 1000751 1001610 1001998 1001953 1000549 1002021 1001367 1001882
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## 1000130 1000135 1000898 1000167 1001364 1001485 1001650 1000071 1001822
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## 1001398 1001431 1001692 1000967 1000201 1000724 1002011 1000185 1002010
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## 1000158 1001313 1001556 1001083 1001065 1001816 1001260 1000675 1001607
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## 1001048 1000321 1001737 1001432 1002015 1001095 1000277 1000270 1001455
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## 1000976 1000038 1000507 1002016 1001765 1000413 1001815 1000295 1001875
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## 1001543 1000554 1000424 1000844 1000395 1001386 1000561 1001734 1001620
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## 1000052 1000588 1000340 1000836 1001164 1001290 1000651 1000107 1001980
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## 1001171 1002001 1000225 1001820 1000150 1000980 1000882 1001567 1001368
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## 1001956 1000878 1001255 1000209 1001864 1000591 1000560 1001677 1000809
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## 1000641 1000355 1001349 1001522 1001511 1000331 1001526 1000753 1000339
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## 1001375 1000727 1000458 1001324 1001837 1001933 1000222 1000079 1001373
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## 1000855 1001322 1000285 1000093 1001597 1001284 1002047 1001427 1000192
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## 1000437 1001792 1001524 1000617 1001175 1001234 1000087 1001326 1001005
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## 1001319 1000625 1001138 1000631 1001730 1000668 1001915 1001154 1000745
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## 1001754 1000403 1001478 1001936 1000587 1001409 1001983 1000856 1000978
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## 1001759 1000243 1001336 1001726 1001372 1000611 1001823 1001477 1001032
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## 1000821 1001766 1000398 1001647 1000096 1000377 1000483 1000613 1000624
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## 1000725 1001833 1001564 1001214 1000481 1000817 1001303 1001881 1000614
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## 1001107 1000032 1001385 1001253 1001144 1000546 1001714 1000234 1000747
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## 1001142 1000194 1000329 1000178 1001797 1001446 1001393 1001024 1000693
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## 1001846 1000607 1001397 1000667 1001259 1001570 1000146 1001555 1001422
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## 1001486 1000548 1001229 1001196 1000964 1000551 1000772 1001584 1001381
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## 1000051 1001879 1000547 1001186 1001981 1000169 1001907 1001454 1000977
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## 1001122 1000991 1001168 1000154 1000925 1001210 1000381 1000278 1000294
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## 1001919 1000470 1001812 1001441 1000595 1000436 1001968 1000144 1000266
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## 1000687 1000367 1000937 1001297 1001425 1000660 1000815 1000620 1001343
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## 1000024 1000674 1000404 1002046 1000533 1001691 1001139 1001942 1000738
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## 1000590 1001015 1001832 1000849 1001497 1001351 1001300 1000215 1000026
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## 1000705 1001037 1000951 1000440 1000795 1001890 1001449 1000260 1000061
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## 1000247 1001899 1000798 1001744 1001311 1000647 1001043 1001371 1001325
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## 1001854 1000303 1000276 1000637 1000742 1000782 1001039 1000297 1001557
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## 1000536 1000172 1000683 1001717 1001802 1000558 1000794 1000752 1000702
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## 1001654 1001224 1000820 1001641 1000720 1000039 1001074 1001082 1001157
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001627 1000933 1001320 1000028 1000226 1000203 1000629 1000670 1001334
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
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## 1001932 1000562 1000240 1001795 1000134 1000423 1000396 1001077 1000566
## [1,] 0 0 0 0 0 0 0 1 0
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## 1001648 1000858 1000412 1001369 1000888 1001342 1001151 1001718 1000085
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## 1001806 1001198 1001594 1000148 1000600 1000070 1000108 1001338 1000224
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## 1000605 1001131 1001500 1001757 1001582 1000999 1001588 1001237 1000784
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## 1000642 1001099 1000152 1000267 1000067 1000924 1000592 1001030 1000498
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## 1001124 1001103 1001090 1001748 1002033 1001572 1001059 1000765 1000221
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## 1001503 1001062 1000679 1001126 1000110 1000006 1000475 1001445 1000390
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## 1002004 1000563 1000444 1001966 1000095 1000638 1000886 1000471 1001220
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## 1001391 1001938 1000974 1000121 1000757 1000517 1000800 1001271 1001181
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## 1001924 1001809 1001857 1001679 1001728 1001878 1000307 1001568 1000327
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## 1001109 1000075 1000543 1000210 1001698 1001982 1000622 1000111 1001013
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## 1001910 1001469 1000692 1001353 1000343 1001521 1000499 1000466 1001293
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 1 0 0 0 0 0 0 0
## 1002000 1000627 1000887 1001763 1001447 1000098 1000506 1000939 1001361
## [1,] 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 1
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000283 1000069 1000577 1001162 1001955 1000948 1000962 1000250 1001533
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000428 1000847 1001604 1001540 1000477 1001678 1001426 1001736 1000769
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 1 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000196 1000474 1000824 1001621 1001749 1000401 1000492 1000137 1000599
## [1,] 0 0 1 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 1 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001952 1002028 1001459 1001755 1000556 1001146 1001098 1001194 1000496
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 1 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1001794 1001529 1000160 1000286 1001360 1000737 1000557 1000149 1000938
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000023 1000872 1001771 1000615 1001937 1001451 1000265 1000736 1000025
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001223 1000956 1001484 1001002 1000468 1001758 1001339 1000695 1000012
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001585 1000467 1001092 1000076 1000010 1002019 1000503 1000166 1000042
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000734 1000703 1001104 1000170 1000269 1001537 1000335 1000202 1001163
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000354 1000078 1000366 1001711 1000383 1001962 1000359 1001066 1001973
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000876 1000420 1000490 1002006 1000033 1001442 1001510 1001629 1001940
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001681 1000369 1000007 1001908 1001954 1001646 1000337 1000479 1000005
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 1 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000003 1001496 1001830 1001595 1002029 1000770 1001921 1001021 1001845
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000298 1000544 1000035 1001862 1000181 1001676 1002034 1001318 1000987
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1002017 1000571 1001017 1001616 1001821 1001244 1001472 1001893 1000570
## [1,] 0 0 0 1 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000094 1001866 1000612 1001052 1001643 1001105 1001606 1000944 1001054
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 1 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000799 1001215 1001009 1000719 1000706 1000626 1000940 1001976 1000330
## [1,] 0 1 1 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1001538 1000729 1001443 1000864 1001614 1000251 1000686 1000616 1001328
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001664 1000322 1000072 1001261 1000104 1002013 1001612 1001167 1002035
## [1,] 0 0 0 0 1 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 1 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000184 1000463 1000949 1000460 1001542 1001452 1001590 1000375 1001876
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 0 0 1 0 0 0 1 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001380 1000541 1000993 1000255 1001404 1000632 1000633 1001027 1001246
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000814 1001498 1002005 1001574 1001348 1001305 1001508 1000352 1000236
## [1,] 0 0 0 0 1 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001541 1001961 1001840 1001814 1001075 1001148 1000103 1000530 1000767
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 1 0 0 0 0 0 0 0
## 1002042 1000758 1000565 1001202 1001581 1000464 1001281 1002025 1002002
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001834 1000013 1000761 1001577 1001930 1000324 1000254 1001067 1000505
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 1 0 1 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000610 1001551 1000238 1001183 1001841 1000253 1001123 1000268 1001501
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0 0 0
## [4,] 0 0 0 0 0 1 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001172 1000982 1001649 1001775 1000162 1000373 1000347 1001410 1000176
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 1 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001732 1000049 1001279 1001309 1000604 1000787 1000713 1001950 1001829
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000807 1001180 1001061 1000027 1000969 1000282 1000309 1001615 1000084
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 1 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1002027 1000252 1001209 1001668 1001056 1000696 1001559 1001863 1001724
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001435 1001254 1001263 1001550 1001741 1001660 1001819 1000586 1000193
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 1 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001429 1000514 1000257 1001121 1000101 1000328 1002023 1000535 1001657
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1000619 1000434 1000183 1001850 1001975 1001927 1000603 1000147 1000348
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 1 0 0 1 0 1 0 0
## 1000851 1001912 1001100 1001799 1000141 1000314 1000846 1000922 1000741
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1001513 1000621 1001633 1000975 1000690 1001704 1001262 1000908 1000207
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001418 1001750 1000364 1001133 1001169 1001073 1001545 1001712 1000358
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000918 1001791 1000835 1000862 1001249 1001877 1000802 1001926 1000159
## [1,] 0 0 0 0 0 0 0 0 1
## [2,] 0 1 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000441 1001565 1000952 1001327 1001873 1001276 1000928 1001793 1001394
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1000892 1001723 1000155 1001669 1000926 1000973 1000950 1000841 1000102
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 1 0 0 0 0
## 1000961 1001947 1000304 1001227 1000733 1000112 1001719 1000415 1002050
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001365 1000037 1000676 1001871 1000125 1000399 1001701 1001554 1000654
## [1,] 0 0 1 0 0 0 1 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000689 1001330 1000272 1000342 1000994 1000397 1000644 1001963 1000091
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001004 1000291 1001535 1000553 1001887 1000489 1000837 1001200 1001856
## [1,] 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 1 0 0 0 0
## [3,] 0 1 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 1 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001238 1001323 1000311 1001515 1001218 1001827 1000755 1001022 1000902
## [1,] 0 0 1 0 1 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000117 1000618 1000785 1001589 1001984 1001127 1001773 1001401 1001715
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001308 1000188 1000572 1000746 1001625 1000893 1001264 1000681 1001402
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001457 1000219 1000796 1000180 1000946 1000929 1000791 1000338 1000284
## [1,] 0 0 1 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 1 0 0 0 0
## [5,] 0 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000931 1000191 1002045 1001093 1000115 1001335 1000863 1000916 1000156
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 1 0 0 0 0 0 0 0 0
## [4,] 0 0 0 1 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000432 1001306 1001414 1001504 1001598 1001923 1000485 1001959 1000790
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 1 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000198 1000157 1001675 1000635 1000353 1001507 1001911 1001240 1001314
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001925 1000810 1001920 1000386 1000034 1000456 1001600 1001628 1001378
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 1 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001097 1001159 1001756 1000231 1001631 1001796 1001278 1000287 1001207
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 1 0 0 0 0
## 1001055 1001089 1000511 1001072 1000639 1001028 1000665 1001733 1000652
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 1 1 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1001645 1001618 1001299 1001179 1001420 1001810 1000242 1000195 1001411
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000500 1001560 1001470 1001778 1001020 1001964 1000539 1000164 1000593
## [1,] 0 0 0 0 0 0 0 1 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001663 1000806 1000389 1001460 1001063 1001195 1000900 1001433 1000715
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000659 1001781 1001285 1000433 1001206 1001707 1001188 1002026 1001064
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000473 1000083
## [1,] 0 0
## [2,] 0 0
## [3,] 0 0
## [4,] 0 0
## [5,] 0 0
## [6,] 0 0head(pheno1)## y sex bmi ybin time status
## 1 -0.6726497 1 25.30159 1 7 1
## 2 0.2171797 2 22.80376 1 9 1
## 3 0.4867783 1 23.83211 0 9 0
## 4 0.3465593 2 27.09918 1 4 1
## 5 -0.9432163 1 21.43145 1 5 1
## 6 0.9721536 2 25.69850 0 7 1head(pheno2)## id y sex bmi
## 10001 10001 -0.68009794 1 24.49436
## 10002 10002 1.04832618 2 22.86157
## 10003 10003 0.04356970 1 27.14200
## 10004 10004 -0.30263426 2 23.90935
## 10005 10005 0.01489937 1 29.21902
## 10006 10006 -1.86419978 2 22.84718head(SNPInfo)## Name gene
## 1 1000001 gene1
## 2 1000002 gene1
## 3 1000003 gene1
## 4 1000004 gene1
## 5 1000005 gene1
## 6 1000006 gene1Perform the burden test that finds genes that contain rare variants that can explain dependent variable y in the two cohorts.
cohort1 <- prepScores(Z=Z1, y~1, SNPInfo=SNPInfo, data=pheno1)
cohort2 <- prepScores(Z=Z2, y~1, SNPInfo=SNPInfo, data=pheno2)
out <- burdenMeta(cohort1, cohort2, SNPInfo = SNPInfo, mafRange=c(0, 0.01))
out$p## [1] 0.804564814 0.046161104 NA NA NA 0.263407302
## [7] NA 0.918255314 NA NA 0.811254045 0.970457899
## [13] 0.004559151 0.131274688 0.722047247 0.766267154 NA NA
## [19] 0.213399304 0.599477839 0.492742980 NA 0.150989236 NA
## [25] 0.400078883 0.337728462 NA 0.106348500 0.678144245 NA
## [31] NA NA 0.128288013 0.982241458 0.673502993 0.333450136
## [37] NA 0.662150090 0.257418803 0.516930816 NA NA
## [43] 0.594097026 0.702123102 0.941726367 0.641861505 0.522236741 0.943271738
## [49] NA NA NA NA NA NA
## [55] 0.744218473 0.501080548 0.364138688 0.857083065 0.659642815 0.716943249
## [61] NA 0.691089146 0.401763495 0.274840325 NA NA
## [67] NA 0.807759418 NA NA 0.839965079 0.066783508
## [73] NA NA 0.417362536 0.600727311 NA NA
## [79] NA 0.971857104 NA NA 0.183859126 NA
## [85] NA 0.922685493 NA 0.662012460 NA 0.484152859
## [91] 0.318236576 NA NA NA NA NA
## [97] 0.949230030 0.345079969 0.203656236 0.897861513burdenMeta() function provided by seqMeta library provides burden test that is based on a linear regression model. The internal computation involves getting the linear regression model lm(y ~ burden + group) when burden is the number of rare variants that exists in a gene of interest in the sample, and from that getting p-value. So burden test is a good way to detecting causal variants of a phenotype if the variants in that region have same directionality in causality with the phenotype.
So as variations of burden test, Combined Multivariate and Collapsing method (CMC); Li and Leal, 2008 and Cohort Allelic Sums Test (CAST); Morgenthaler and Thilly, 2007, etc. exist.
2-2. Single Variant Burden Test Using EPACTS (Efficient and Parallelizable Association Container Toolbox)
EPACTS (Efficient and Parallelizable Association Container Toolbox) is an anlytical tool that supports single nucleotide variant-level burden tests as well as gene-perspective and case-perspective burden tests.
It uses VCF files that contain the genomic variations and PED files that contain phenotype with pedigree information. The threshold for rare variant is set at less than MAF 1% with --min-maf argument. The input VCF file is --vcf 1000G_exome_chr20_example_softFiltered.calls.vcf.gz that contains chromosome 20 of 1000 genomes project’s information. The input PED file is --ped 1000G_dummy_pheno.ped.
[soh1@x020 chapter6]$ cd RareVariant
[soh1@x020 RareVariant]$ ls
data out plot snp2hla vcftabix -p vcf data/1000G_exome_chr20_example_softFiltered.calls.vcf.gzWe need EPACTS before proceeding, so download the latest version from EPACTS github at https://github.com/statgen/EPACTS through git and install. This is so called “clone the repo and build it” command.
[soh1@x020 RareVariant]$ git clone https://github.com/statgen/EPACTS
Cloning into 'EPACTS'...
remote: Enumerating objects: 1449, done.
remote: Total 1449 (delta 0), reused 0 (delta 0), pack-reused 1449
Receiving objects: 100% (1449/1449), 172.57 MiB | 15.60 MiB/s, done.
Resolving deltas: 100% (563/563), done.
Checking out files: 100% (518/518), done.gda@GDA： 〜/RareVariant$ epacts single —-vcf data/1000G_exome_chr20_example_softFiltered.calls.vcf.gz ——ped data/1000G_dummy_pheno.ped --min-mat 0.001 --chr 20 --pheno DISEASE --cov AGE --cov SEX --test b.score --anno --out out/test.single.b.score --run 2This results in top 5000 association study results and performs quantile-quantile graph and Manhattan graph analysis per MAF.
zcat out/test.single.b.score.epacts.gz | headhead out/test.single.b.score.epacts.top5000The resulting file contains following contents:
- NS: Number of Phenotype Samples with that Genotype
- AC: Number of Total Reference Alternative Alleles
- CALLRATE: Rate of non-missing genotypes called successfully
- MAF: Minor Allele Frequency
- PVALUE: p-value of Single Nucleotide Variant test
- AF.CASE: Allele frequency of experimental group variants
- AF.CTRL: Allele frequency of control group variants
epacts anno --in data/1000G_exome_chr20_example_softFiltered.calls.vcf.gz --out data/1000G_exome_chr20_example_sfotFiltered.calls.anno.vcf.gzepacts group --vcf data/1000G_exome_chr20_example_softFiltered.calls.anno.vcf.gz --groupf data/1000G_exome_chr20_exapmle_softFiltered.calls.anno.grp --out out/test.gene.skat --ped data/100G_dummy_pheno.ped --max-maf 0.05 --sepchr 20 --pheno QT --cov AGE --cov SEX --test skat --skat-o --run 2So, apparently SKAT is a test for association between a set of rare (and common) variant and continuous/dichotomous phenotypes using kernel machine methods. Here’s the homepage.
- NS: Phenotype sample number that has such genotypes
- FRAC_WITH_RARE: Fraction of individuals with rare variants
- NUM_ALL_VARS: number of variants that defines a group
- NUM_PASS_VARS: –min-maf, –min-mac, –max-maf, –min-callrate. Number of variants containing these thresholds
- NUM_SING_VARS: Number of singletons that correspond to variants in NUM_PASS_VARS.
- PVALUE: P-value of burden test
2-3. SKAT Association Study
Apply SKAT (Sequence Kernel Association Test) to the same seqMetaExample dataset. SKAT uses distribution elements of random effect model.
cohort1 <- prepScores(Z=Z1, y~sex+bmi, SNPInfo = SNPInfo, data=pheno1)
cohort2 <- prepScores(Z=Z2, y~sex+bmi, SNPInfo = SNPInfo, kins=kins, data=pheno2)
out.skat <- skatMeta(cohort1, cohort2, SNPInfo=SNPInfo)
out.skat[order(out.skat$p), ]
SNPInfo variable contains in which genes each variant is contained.
We use sex and bmi variables as covariates to perform SKAT test. Even in Burden test you can designate covariates if you write y~sex+bmi instead of y~1. SKAT method calculates the score of specific gene or region by considering how variants are distributed. Therefore, unlike burden test, it can catch signal even if the variants are not oriented towards particular directionality in causality. Genes gene98, gene28, etc. explain the dependent variable y well and these are the significant rare variant genes associated with rare diseases.
2-3. SKAT-O Association Study
SKAT-O uses advantages of both burden test and SKAT to optimize statistical power. SKAT-O’s O means ‘optimal’ and it corrects for type-I errors that occur when sample size is small. Usage is same as SKAT, and you use skatOMeta() instead of skatMeta().
out.skat <- skatOMeta(cohort1, cohort2, SNPInfo = SNPInfo)
out.skat[order(out.skat$p), ]3. Linkage Disequilibrium Data Analysis
Let’s calculate LD from publicly available data that is from 1000 genomes project. We use VCF of 104 JPT people’s data but if you’ve got enough time, it’s better for you to calculate LD from many more data like EAS 504. We check if we’ve got the necessary files. The VCF file has already been extracted with variants between position of chr16:54000000-54050000.
[soh1@x020 RareVariant]$ ls
data EPACTS out plot snp2hla vcf
[soh1@x020 RareVariant]$ cd vcf
[soh1@x020 vcf]$ ls
JPT_part.vcf.gz JPT_part.vcf.gz.tbi3-1. PED/MEP file formats
Let’s talk about PLINK input format. First of all, we’ve got *.PED (BED) that contains pedigree, genotype, and phenotype data. So we have total of 6 + 208 columns,
- Column 1 = Family ID
- Column 2 = Individual ID
- Column 3 = Paternal ID (when it’s 0, missing)
- Column 4 = Mataernal ID (when it’s 0, missing)
- Ciolumn 5 = Sex
- Column 6 = Phenotype (1, 2, or 0; 1 = unaffected, 2= affected, 0 = missing)
- Columns 7 + 8 = Genotype pair of SNP1 (missing if 0)
- Columns 9 + 10 = Genotype pair of SNP2 (missing if 0)
Now, *.MAP file contains the variant information of each.
- Column 1 = chromosome number
- Column 2 = SNP ID
- Column 3 = Genetic Distance (morgans)
- Column 4 = physical base-pair position (bp)
The two files have relationship as described below.
3-2. Convert from VCF to PED
[soh1@x020 vcf]$ vcftools --gzvcf JPT_part.vcf.gz --plink-tped --out JPT --phased
VCFtools - v0.1.12b
(C) Adam Auton and Anthony Marcketta 2009
Parameters as interpreted:
--gzvcf JPT_part.vcf.gz
--out JPT
--phased
--plink-tped
Using zlib version: 1.2.3
Versions of zlib >= 1.2.4 will be *much* faster when reading zipped VCF files.
After filtering, kept 104 out of 104 Individuals
Writing PLINK TPED file ... PLINK-TPED: Only outputting biallelic loci.
Writing PLINK TFAM file ... Done.
After filtering, kept 1388 out of a possible 1388 Sites
Run Time = 0.00 seconds
[soh1@x020 vcf]$ ls
JPT.log JPT_part.vcf.gz JPT_part.vcf.gz.tbi JPT.tfam JPT.tpedYou can see that there are resulting ouput files (*.log, *.tped, *.tfam). The very first four columns in the *.tped file contains variant information and the 208 columns that follow contain alleles of 104 people. Each of the pairs of bases cut sequentially represent one person’s genotype. *.tfam file represents one person per one row, and contains information about individuals and families. Each of the six columns mean Family ID, Individual ID, Paternal ID, Maternal ID, Sex (1=male, 2=female, other=unknown), Phenotype.
[soh1@x020 vcf]$ more JPT.tped
16 rs150805752 0 54000022 C C C C C C C C C C C C C C C C C C C C CC
16 rs139198525 0 54000023 G G G G G G G G G G G G G G G G G G G G GG
16 16:54000027 0 54000027 A A A A A A A A A A A A A A A A A A A A AA
16 16:54000078 0 54000078 T T T T T T T T T T T T T T T T T T T T TT
16 16:54000108 0 54000108 T T T T T T T T T T T T T T T T T T T T TT
16 rs143690163 0 54000121 C C C C C C C C C C C C C C C C C C C C C
--More--(0%)[soh1@x020 vcf]$ more JPT.tfam
EAS_JPT_NA18939_F EAS_JPT_NA18939_F 0 0 0 0
EAS_JPT_NA18940_M EAS_JPT_NA18940_M 0 0 0 0
EAS_JPT_NA18941_F EAS_JPT_NA18941_F 0 0 0 0
EAS_JPT_NA18942_F EAS_JPT_NA18942_F 0 0 0 0
EAS_JPT_NA18943_M EAS_JPT_NA18943_M 0 0 0 0
EAS_JPT_NA18944_M EAS_JPT_NA18944_M 0 0 0 0
EAS_JPT_NA18945_M EAS_JPT_NA18945_M 0 0 0 0
EAS_JPT_NA18946_F EAS_JPT_NA18946_F 0 0 0 0
EAS_JPT_NA18947_F EAS_JPT_NA18947_F 0 0 0 0
EAS_JPT_NA18948_M EAS_JPT_NA18948_M 0 0 0 0
EAS_JPT_NA18949_F EAS_JPT_NA18949_F 0 0 0 0
EAS_JPT_NA18950_F EAS_JPT_NA18950_F 0 0 0 0
EAS_JPT_NA18951_F EAS_JPT_NA18951_F 0 0 0 0
EAS_JPT_NA18952_M EAS_JPT_NA18952_M 0 0 0 0
EAS_JPT_NA18953_M EAS_JPT_NA18953_M 0 0 0 0
EAS_JPT_NA18954_F EAS_JPT_NA18954_F 0 0 0 0
EAS_JPT_NA18956_F EAS_JPT_NA18956_F 0 0 0 0
EAS_JPT_NA18957_F EAS_JPT_NA18957_F 0 0 0 0
EAS_JPT_NA18959_M EAS_JPT_NA18959_M 0 0 0 0
EAS_JPT_NA18960_M EAS_JPT_NA18960_M 0 0 0 0
EAS_JPT_NA18961_M EAS_JPT_NA18961_M 0 0 0 0
EAS_JPT_NA18962_M EAS_JPT_NA18962_M 0 0 0 0
EAS_JPT_NA18963_F EAS_JPT_NA18963_F 0 0 0 0
EAS_JPT_NA18964_F EAS_JPT_NA18964_F 0 0 0 0
EAS_JPT_NA18965_M EAS_JPT_NA18965_M 0 0 0 0
EAS_JPT_NA18966_M EAS_JPT_NA18966_M 0 0 0 0
EAS_JPT_NA18967_M EAS_JPT_NA18967_M 0 0 0 0
EAS_JPT_NA18968_F EAS_JPT_NA18968_F 0 0 0 0
EAS_JPT_NA18969_F EAS_JPT_NA18969_F 0 0 0 0
EAS_JPT_NA18970_M EAS_JPT_NA18970_M 0 0 0 0
EAS_JPT_NA18971_M EAS_JPT_NA18971_M 0 0 0 0
EAS_JPT_NA18972_F EAS_JPT_NA18972_F 0 0 0 0
--More--(30%)I downloaded plink binary executable from plink download page, named plink-1.07-x86_64.zip v1.07.
And unzipped the binary file with,
unzip plink-1.07-x86_64.
Then
[soh1@x020 vcf]$ ls
JPT.log JPT_part.vcf.gz JPT_part.vcf.gz.tbi JPT.tfam JPT.tped plink-1.07-x86_64Then I executed plink, giving arguments about –tped, –tfam, –make-bed, –out, and especially –noweb that tells plink not to go online to check for the latest version of plink.
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --tped JPT.tped --tfam JPT.tfam --make-bed --out ./JPT --noweb
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ ./JPT.log ]
Analysis started: Fri Aug 28 13:26:46 2020
Options in effect:
--tped JPT.tped
--tfam JPT.tfam
--make-bed
--out ./JPT
--noweb
** For gPLINK compatibility, do not use '.' in --out **
Reading pedigree information from [ JPT.tfam ]
104 individuals read from [ JPT.tfam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
Writing list of these individuals to [ ./JPT.nosex ]
1380 (of 1380) markers to be included from [ JPT.tped ]
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
Writing pedigree information to [ ./JPT.fam ]
Writing map (extended format) information to [ ./JPT.bim ]
Writing genotype bitfile to [ ./JPT.bed ]
Using (default) SNP-major mode
Analysis finished: Fri Aug 28 13:26:46 2020No we get binary BED, BIM, FAM files as output files. JPT.bed file’s column corresponds to an SNP, first four columns are SNPs, and 208columns are alleles.
JPT.bed file is a binary file with genotypes in it, so we can’t read it directly. JPT.bim contains alternative allele names and it’s an extended MAP file.
ALL.chr16.JPT.fam file, like ped file, has 6 columns (Family ID, Individual ID, Paternal ID, Maternal ID, Sex, Phenotype). JPT.nosex file contains two columns, which are Family ID and Individual ID.
[soh1@x020 vcf]$ more JPT.bim
16 rs150805752 0 54000022 0 C
16 rs139198525 0 54000023 0 G
16 16:54000027 0 54000027 0 A
16 16:54000078 0 54000078 0 T
16 16:54000108 0 54000108 0 T
16 rs143690163 0 54000121 0 C
16 16:54000185 0 54000185 0 G
16 rs373699250 0 54000190 0 T
16 rs147458024 0 54000198 T C
16 rs139841196 0 54000220 0 A
16 16:54000243 0 54000243 0 T
16 rs145462994 0 54000261 T A
16 16:54000380 0 54000380 0 C
16 rs147689010 0 54000381 0 A
16 16:54000430 0 54000430 0 T
16 16:54000521 0 54000521 0 G
16 rs7199210 0 54000588 0 A
16 rs148777468 0 54000672 0 G
16 16:54000765 0 54000765 0 C
16 16:54000772 0 54000772 0 C
16 rs73614162 0 54000773 0 G
16 rs1344502 0 54000792 G A
16 16:54000858 0 54000858 0 G
16 16:54000889 0 54000889 0 G
16 rs190638462 0 54000900 0 G
16 rs1111483 0 54000907 C A
16 16:54000953 0 54000953 0 G
16 rs181596393 0 54001000 0 G
16 16:54001001 0 54001001 0 C
16 16:54001005 0 54001005 0 G
16 16:54001010 0 54001010 0 G
16 rs186152990 0 54001028 0 G
--More--(2%)[soh1@x020 vcf]$ head JPT.fam
EAS_JPT_NA18939_F EAS_JPT_NA18939_F 0 0 0 -9
EAS_JPT_NA18940_M EAS_JPT_NA18940_M 0 0 0 -9
EAS_JPT_NA18941_F EAS_JPT_NA18941_F 0 0 0 -9
EAS_JPT_NA18942_F EAS_JPT_NA18942_F 0 0 0 -9
EAS_JPT_NA18943_M EAS_JPT_NA18943_M 0 0 0 -9
EAS_JPT_NA18944_M EAS_JPT_NA18944_M 0 0 0 -9
EAS_JPT_NA18945_M EAS_JPT_NA18945_M 0 0 0 -9
EAS_JPT_NA18946_F EAS_JPT_NA18946_F 0 0 0 -9
EAS_JPT_NA18947_F EAS_JPT_NA18947_F 0 0 0 -9
EAS_JPT_NA18948_M EAS_JPT_NA18948_M 0 0 0 -9[soh1@x020 vcf]$ head JPT.nosex
EAS_JPT_NA18939_F EAS_JPT_NA18939_F
EAS_JPT_NA18940_M EAS_JPT_NA18940_M
EAS_JPT_NA18941_F EAS_JPT_NA18941_F
EAS_JPT_NA18942_F EAS_JPT_NA18942_F
EAS_JPT_NA18943_M EAS_JPT_NA18943_M
EAS_JPT_NA18944_M EAS_JPT_NA18944_M
EAS_JPT_NA18945_M EAS_JPT_NA18945_M
EAS_JPT_NA18946_F EAS_JPT_NA18946_F
EAS_JPT_NA18947_F EAS_JPT_NA18947_F
EAS_JPT_NA18948_M EAS_JPT_NA18948_M3-3. Calculating Linkage Disequilibrium
Now calculate the LD relationship between SNPs rs11646260 and rs59578934.
--noweb: block web connection and run on local --bfile: get the binary file generated in the previous step --ld: prints the LD relationship calculated between two SNPs
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --noweb --bfile JPT --ld rs11646260 rs59578934
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ plink.log ]
Analysis started: Fri Aug 28 13:40:20 2020
Options in effect:
--noweb
--bfile JPT
--ld rs11646260 rs59578934
Reading map (extended format) from [ JPT.bim ]
1380 markers to be included from [ JPT.bim ]
Reading pedigree information from [ JPT.fam ]
104 individuals read from [ JPT.fam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
These individuals will be set to missing ( or use --allow-no-sex )
Writing list of these individuals to [ plink.nosex ]
Reading genotype bitfile from [ JPT.bed ]
Detected that binary PED file is v1.00 SNP-major mode
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
LD information for SNP pair [ rs11646260 rs59578934 ]
R-sq = 0.015 D' = 0.998
Haplotype Frequency Expectation under LE
--------- --------- --------------------
GC 0.014 0.007
AC 0.000 0.007
GT 0.471 0.479
AT 0.514 0.507
In phase alleles are GC/AT
Analysis finished: Fri Aug 28 13:40:20 2020So if you look at the section where it begins to say “LD information for SNP pair”, GC/AT are predicted as in phase alleles.
Now do the same for different positions.
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --noweb --bfile JPT --ld rs11646260 rs8063575
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ plink.log ]
Analysis started: Fri Aug 28 13:45:46 2020
Options in effect:
--noweb
--bfile JPT
--ld rs11646260 rs8063575
Reading map (extended format) from [ JPT.bim ]
1380 markers to be included from [ JPT.bim ]
Reading pedigree information from [ JPT.fam ]
104 individuals read from [ JPT.fam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
These individuals will be set to missing ( or use --allow-no-sex )
Writing list of these individuals to [ plink.nosex ]
Reading genotype bitfile from [ JPT.bed ]
Detected that binary PED file is v1.00 SNP-major mode
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
LD information for SNP pair [ rs11646260 rs8063575 ]
R-sq = 0.943 D' = 0.980
Haplotype Frequency Expectation under LE
--------- --------- --------------------
GG 0.481 0.238
AG 0.010 0.252
GA 0.005 0.247
AA 0.505 0.262
In phase alleles are GG/AA
Analysis finished: Fri Aug 28 13:45:46 2020R-sq value is the LD index, it assumes SNPs that have the square of correlation coefficient that is bigger than a set value as the tag SNPs. It’s between 0 to 1 and 0 means complete linkage equilibrium and 1 means complete linkage disequilibrium. If it’s over 1/3, it’s usually called as a strong LD.
\(0 \textrm{(complete LE)}<1/3 \textrm{(cutoff for a pretty strong LD)}<\textrm{R-sq}<1 \textrm{(complete LD)}\)
D’ value is also an LD index. If it’s equal to 1, it’s complete LD, if it’s equal to 0, then it’s complete LE. If it’s less than 1, somewhere along the previous generations there were genetic recombinations.
\(0 \textrm{(complete LE)}<\textrm{D'}\textrm{(Gene recombination occurred somewhere in previous generations)}<1 \textrm{(complete LD)}\)
Now compute LDs for all possible variant pairs along 54000000 to 54050000 bp in chromosome 16.
Usage Reminder:
- –bfile: get binary file from previous steps
- –chr: input chromosome position
- –from-bp: input the position of starting base
- –to-bp: input the position of end base
- –ld-snp: get the reference SNPs for LD computation
- –r2: calculate r2 value using the phased haplotypes
- –ld-window-r2: the r2 value used for filtering result
- –ld-window: the maximum number of SNPs between the SNPs used for calculating LD. the LD is for result filtering
- –ld-window-kb: maximum physical distance (in kb) between the SNPs used for calculating LD. the LD is for result filtering
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --bfile JPT --chr 16 --from-bp 54000000 --to-bp 54050000 --ld-snp rs11646260 --r2 --ld-window-r2 0 --ld-window 999999 --ld-window-kb 99999 --noweb --out ./JPT
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ ./JPT.log ]
Analysis started: Fri Aug 28 14:01:28 2020
Options in effect:
--bfile JPT
--chr 16
--from-bp 54000000
--to-bp 54050000
--ld-snp rs11646260
--r2
--ld-window-r2 0
--ld-window 999999
--ld-window-kb 99999
--noweb
--out ./JPT
** For gPLINK compatibility, do not use '.' in --out **
Reading map (extended format) from [ JPT.bim ]
1380 markers to be included from [ JPT.bim ]
Scan region on chromosome 16 from [ rs150805752 ] to [ 16:54049880 ]
Reading pedigree information from [ JPT.fam ]
104 individuals read from [ JPT.fam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
These individuals will be set to missing ( or use --allow-no-sex )
Writing list of these individuals to [ ./JPT.nosex ]
Reading genotype bitfile from [ JPT.bed ]
Detected that binary PED file is v1.00 SNP-major mode
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
Writing LD statistics to [ ./JPT.ld ]
Analysis finished: Fri Aug 28 14:01:28 2020[soh1@x020 vcf]$ ls
JPT.bed JPT.fam JPT.log JPT_part.vcf.gz JPT.tfam plink-1.07-x86_64 plink.nosex
JPT.bim JPT.ld JPT.nosex JPT_part.vcf.gz.tbi JPT.tped plink.log[soh1@x020 vcf]$ head JPT.ld
CHR_A BP_A SNP_A CHR_B BP_B SNP_B R2
16 54032493 rs11646260 16 54000198 rs147458024 1.87066e-05
16 54032493 rs11646260 16 54000261 rs145462994 1.87066e-05
16 54032493 rs11646260 16 54000792 rs1344502 0.0213057
16 54032493 rs11646260 16 54000907 rs1111483 0.0213057
16 54032493 rs11646260 16 54001529 rs192014550 1.87066e-05
16 54032493 rs11646260 16 54002172 rs140765996 3.778e-05
16 54032493 rs11646260 16 54002294 16:54002294 5.72312e-05
16 54032493 rs11646260 16 54002356 rs144710532 0.0428216
16 54032493 rs11646260 16 54002845 rs59578934 5.72312e-053-4. Visualizing LD with SNPplotter
So we calculated LDs for all possible combinations of allele pairs. Print out the graph for the computed LD. Install snp.plotter for LD graph printing and execute the following command. This is an example of drawing haplotype SNP sets and LD graph on two racial groups.
Install Xming instead of Xmanager for opensource viewing of server screen display.
Intsall snp.plotter R package and then execute plotting.
[soh1@x020 vcf]$ cd ..
[soh1@x020 RareVariant]$ cd plot
[soh1@x020 plot]$ ls
config.txt d1_hap.txt d1_ss.txt d2_hap.txt d2_ss.txt null_d1_controls.dat null_rsq_phys_color.pdf palette.txt
[soh1@x020 plot]$ R
> library(snp.plotter)
Loading required package: grid
> snp.plotter(config.file="config.txt")
START READ.CONFIG
FINISH READ.CONFIG
START CREATE.COLOR.LIST
FINISH CREATE.COLOR.LIST
START CREATE.SYMBOL.LIST
FINISH CREATE.SYMBOL.LIST
START RETRIEVE.DATA
START SET.IMAGE.PARAMETERS
FINISH SET.IMAGE.PARAMETERS
START FIX.VALUES
FINISH FIX.VALUES
START SET.IMAGE.PARAMETERS
FINISH SET.IMAGE.PARAMETERS
START FIX.VALUES
FINISH FIX.VALUES
START DRAW.PLOT.GRID.SETUP
FINISH DRAW.PLOT.GRID.SETUP
START FIX.VALUES
FINISH FIX.VALUES
START DRAW.PLOT.GRID.SNP.NAMES
FINISH DRAW.PLOT.GRID.SNP.NAMES
START DRAW.PLOT.GRID.SS
FINISH DRAW.PLOT.GRID.SS
START DRAW.PLOT.GRID.HAP
FINISH DRAW.PLOT.GRID.HAP
START FIX.VALUES
FINISH FIX.VALUES
START DRAW.PLOT.GRID.SS
FINISH DRAW.PLOT.GRID.SS
START DRAW.PLOT.GRID.HAP
FINISH DRAW.PLOT.GRID.HAP
FINISH RETRIEVE.DATA
START DRAW.LEGEND
FINISH DRAW.LEGEND
START DRAW.PLOT.LD.PLOT
FINISH DRAW.PLOT.LD.PLOTYou can see that the R library runs on a config file config.txt. It’s got following contents:
[soh1@x020 plot]$ cat config.txt
SNP.FILE=d1_ss.txt,d2_ss.txt
HAP.FILE=d1_hap.txt,d2_hap.txt
PALETTE.FILE=palette.txt
EVEN.SPACED=FALSE
USE.GBL.PVAL=TRUE
DISP.HAP=TRUE
DISP.LDMAP=TRUE
LD.COLOR.SCHEME=heat
COLOR.LIST=red,blue
SYMBOLS=circle-fill,square-fill
PVAL.THRESHOLD=1
LAB.Y=log
GENOTYPE.FILE=null_d1_controls.dat
LD.TYPE=rsquare
DISP.COLOR.BAR=TRUE
DISP.TYPE=symbol
DISP.LEGEND=TRUE
SAMPLE.LABELS=Pop.1,Pop.2
IMAGE.TYPE=pdf
DISP.SNP=TRUE
DISP.MULT.LAB.X=FALSE
IMAGE.TITLE=" "
IMAGE.NAME=null_rsq_phys_color
IMAGE.SIZE=3.5
CONNECTING.LINES.FACTOR=1.5
DISP.PHYS.DIST=TRUE
CONNECTING.LINES.ADJ=0.02SNP.FILE: tab-delimited text file that’s got p-values of single SNPs. It’s got columns of SNP.NAME, LOC, SS.PVAL. ASSOC shows whether it is a allele for disease risk or prevention. SNP.NAME shows the name of that SNP, LOC means locus, SS.PVAL means p-value of that particular SNP. Examples are like the following:
[soh1@x020 plot]$ less d1_ss.txt
ASSOC SNP.NAME LOC SS.PVAL
+ rs0000001 50017600 0.0082
+ rs0000002 50056889 0.0101
+ rs0000003 50343044 0.00754
+ rs0000004 50373804 0.0391
+ rs0000005 50375238 2.58E-05
+ rs0000006 50492148 0.0128
+ rs0000007 50522339 0.0504
+ rs0000008 50542551 0.222
+ rs0000009 50623862 0.00269
+ rs00000010 50646467 0.0695
+ rs00000011 50658231 0.341
+ rs00000012 50664029 0.0114
+ rs00000013 50677804 0.000548
+ rs00000014 50715691 0.00111
+ rs00000015 50746424 0.131
+ rs00000016 50766173 0.829
+ rs00000017 51127051 0.926
+ rs00000018 51273874 0.548
+ rs00000019 51348270 0.641
+ rs00000020 51375954 0.817
d1_ss.txt (END)[soh1@x020 plot]$ less d1_hap.txt
HAP.FILE: tab-delimited file that has haplotype p-value, AAOC, G.PVAL, I.PVAL. G.PVAL shows global p-value of each haplotype, I.PVAL shows individual p-value.
LD.TYPE: For LD measurement there are two options: dprime or rsquare. dprime and rsquare
All the other options can be properly controlled with Display option. LD graph resulting from the example files are as follows (null_rsq_phys_color.pdf)
IMAGE.NAME=null_rsq_phys_color option in configuration file.
[soh1@x020 plot]$ okular null_rsq_phys_color.pdf
So, to explain this data, note that the above exercise is taken from an article on bioinformatics: “snp.plotter: an R-based SNP/haplotype association and linkage disequilibrium plotting package”. The HapMap project catalogs SNPs from populations with African, Asian and European ancestry (The International HapMap Consortium, 2005). Sample data for 20 SNPs was obtained from HapMap and two case-control populations with 500 cases and 500 controls were simulated using the Simulation of Haplotype Heterogeneity, Interaction and Population Stratification (SH2IPS) R package.
If the SNPs have same p-values, that is interpreted as there’s a linkage disequilibrium and the loci are associated with each other.
Dotted lines represent P-value thresholds.
4. HLA alternative alleles, HLA SNPs and Imputation of Amino Acid Polymorphisms in HLA
HLA gene is an important gene that dictates the graft (organ transplantation) success rate, and it has been identified as one of the largest risk factor in autoimmune diseases in multiple GWAS studies.
However, it shows a wide spectrum of polymorphisms and genotype determination is difficult, so is still remaining as one of bioinformatics’s biggest challenges.
Most of the current standard NGS technologies do not guarantee sequencing results of HLA regions. Therefore, if we can imputate the insufficient information and estimate which genes among the HLA genes and which variants are associated with a particular disease, then it would greatly help looking for disease antigens and excavating disease target genes.
There have been quite a number of algorithms suggested, but SNP2HLA (Imputation of Amino Acid Polymorphisms in Human Leukocyte Antigens) that was published in 2014 was distinguishable from other algorithms in that it utilized the intergenic SNPs that exist between HLA genes and comparing that to the reference sequence to imputate the missing HLA genotype information. So now we dive into SNPs of HLA genes and amino acid polymorphism imputation.
Now, we gotta use the .csh^[C shell, csh, is a shell of UNIX. It’s more powerful and convenient in user-experience compared to original bourne-shell (sh). It is based on C and has powerful program writing/editing features, therefore called “C shell”. Most representative functions include history, nickname, process control, etc. 1.CSH is C shell while BASH is Bourne Again shell. 2. C shell and BASH are both Unix and Linux shells. While Clibrary(seqMeta)
```r
data(seqMetaExample)head(Z1)## 1001797 1000452 1001692 1000219 1000679 1001623 1001799 1001243 1001421
## [1,] 0 0 0 1 0 0 0 0 0
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## 1000028 1000303 1000423 1000231 1001013 1001821 1001306 1000860 1000526
## [1,] 0 0 0 0 0 0 0 0 0
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## 1000459 1001373 1001269 1000507 1001562 1000788 1001567 1000023 1000032
## [1,] 0 0 1 0 0 0 0 0 0
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## 1000416 1001765 1000491 1002005 1000362 1000926 1000346 1000306 1001290
## [1,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 1 0 0 0
## 1000951 1001048 1000212 1001253 1000071 1001297 1001078 1000337 1001437
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001228 1000620 1000892 1000914 1001527 1001275 1001432 1000710 1001611
## [1,] 0 0 0 0 0 0 0 0 0
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## [1,] 0 0 0 0 0 0 0 0 0
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## [1,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001268 1001162 1001944 1000833 1001747 1001159 1001258 1000555 1001450
## [1,] 0 0 0 0 0 0 1 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000188 1001870 1000197 1000518 1000824 1001485 1000046 1000596 1001848
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001233 1000057 1001714 1001639 1000944 1002035 1000105 1000674 1001281
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001545 1001729 1000394 1000568 1001853 1001504 1001340 1001876 1001583
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1000640 1000959 1001178 1000830 1000955 1001877 1000011 1001999 1000699
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 1
## [5,] 0 0 0 1 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001166 1001642 1000073 1000862 1000952 1001785 1001791 1000538 1001015
## [1,] 0 1 0 1 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 1 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000287 1001331 1000920 1000097 1001059 1000644 1000719 1001740 1000286
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 1 0
## 1001638 1001487 1001371 1000836 1000462 1001082 1000198 1000396 1001370
## [1,] 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 1 0 1 0 0 0
## [6,] 0 0 0 0 0 0 1 0 0
## 1001154 1001866 1001647 1001533 1001625 1001231 1001673 1000675 1000037
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 1 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001145 1000093 1001563 1001558 1001949 1001469 1001631 1001130 1001634
## [1,] 0 0 0 0 0 0 0 1 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 1 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001652 1002009 1001347 1001484 1000781 1001808 1000009 1000961 1001330
## [1,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000490 1001447 1000561 1001138 1000629 1000503 1001235 1000556 1000434
## [1,] 0 0 0 0 0 0 0 0 0
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## 1000571 1001506 1000425 1000205 1000256 1000193 1000199 1001391 1001213
## [1,] 0 1 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000418 1000586 1000349 1001359 1001353 1000127 1000317 1001761 1000141
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## 1000637 1000846 1001252 1002040 1001298 1000815 1001574 1001176 1000427
## [1,] 0 0 0 0 0 1 0 0 0
## [2,] 0 1 0 0 0 0 0 0 0
## [3,] 1 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000065 1000923 1000043 1001742 1000468 1001137 1000110 1001902 1001792
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
## [3,] 0 0 1 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001413 1001619 1001006 1000319 1001794 1000426 1000980 1001460 1000554
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000983 1001080 1001915 1001534 1001705 1000406 1001153 1000035 1000084
## [1,] 0 0 0 0 0 0 0 0 0
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## [4,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 1 0
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## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 1 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000192 1001123 1000022 1001399 1000001 1001535 1001697 1000487 1000605
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001569 1000610 1001050 1001175 1000796 1000058 1001379 1001905 1000463
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001483 1001518 1000701 1001617 1000658 1001482 1001410 1001699 1000486
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 1 0 0 0 1 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 1 0 0 1
## 1001089 1001846 1001390 1000552 1000549 1001609 1001087 1000111 1000970
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 1 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000283 1000051 1000947 1000048 1001466 1000125 1001093 1000234 1000079
## [1,] 0 0 0 0 0 0 0 0 0
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## 1000320 1000273 1001819 1001414 1001426 1001032 1000392 1002006 1000201
## [1,] 0 0 0 0 0 0 0 0 0
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## 1000330 1000168 1001577 1000622 1001385 1000953 1001115 1000228 1002004
## [1,] 0 0 0 0 0 0 0 0 0
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## 1002048 1000757 1001986 1000611 1000432 1000602 1000888 1001733 1000250
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 1 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001198 1002013 1001067 1001328 1001157 1001038 1000519 1000563 1000594
## [1,] 0 0 0 0 0 0 0 0 0
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## [3,] 0 1 0 0 0 0 1 0 0
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## 1001242 1001813 1000152 1000184 1001261 1001946 1001106 1000832 1001264
## [1,] 0 0 0 0 0 0 0 0 0
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## [1,] 0 0 0 0 0 1 0 0 0
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## [3,] 0 0 0 0 0 0 0 0 0
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## 1002045 1001147 1000720 1001244 1001481 1001947 1000333 1000453 1000747
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 1 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000379 1001210 1001994 1001885 1000777 1000322 1000802 1000196 1000598
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 1 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000460 1000734 1001772 1001222 1001039 1001076 1000052 1001878 1000299
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## 1000039 1000067 1001090 1000517 1001897 1000313 1000061 1001472 1000498
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## 1000269 1001150 1001037 1000280 1001507 1001710 1001148 1001288 1001596
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## 1000965 1001321 1001084 1000725 1001107 1000823 1001774 1001995 1000528
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## 1000336 1001169 1001872 1000327 1000020 1000060 1000448 1001767 1000289
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## 1001118 1001259 1000068 1000229 1000889 1001307 1000101 1000076 1001129
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## 1000969 1001626 1000787 1000412 1000282 1000671 1001336 1000324 1001616
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## 1000932 1000489 1000276 1000901 1000891 1000343 1001271 1000140 1000730
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## 1000226 1001382 1001836 1001366 1000018 1000790 1001595 1000041 1001342
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## 1000496 1001615 1000104 1000420 1000581 1000357 1000559 1000251 1000433
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## 1001302 1001383 1000779 1001376 1000288 1001734 1001781 1001539 1000897
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## 1000842 1000363 1001800 1001127 1000645 1001543 1000163 1000977 1001216
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## 1000648 1001603 1000262 1000912 1000094 1001002 1001972 1001630 1000925
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## 1001119 1000013 1001950 1001250 1001134 1001981 1001214 1001708 1001687
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## 1001387 1001811 1001520 1000562 1000064 1001014 1001349 1000493 1000066
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## 1000190 1001179 1001688 1000464 1000814 1001553 1000948 1000165 1001197
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## 1000756 1000960 1001144 1001282 1000599 1001815 1000395 1001657 1001422
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## 1000845 1000014 1000560 1000957 1001719 1001081 1001758 1000935 1000909
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## 1000797 1001587 1000612 1000680 1000991 1001375 1001825 1002032 1001810
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## 1000450 1001012 1000869 1001959 1001036 1001283 1001128 1001671 1001523
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## 1001335 1001956 1000027 1000421 1000683 1000218 1000746 1000981 1000270
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## 1001446 1001361 1001451 1000413 1000936 1001095 1000082 1000593 1001133
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## 1001381 1000441 1001736 1000649 1000818 1001136 1001556 1001181 1000467
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## 1001911 1001291 1000044 1001018 1001304 1001368 1000369 1000036 1001239
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## 1000987 1001114 1001510 1001406 1000442 1001338 1000996 1001498 1000580
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## 1001163 1001546 1001143 1000785 1000853 1000261 1001423 1001088 1000750
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## 1001869 1000775 1000539 1000470 1001255 1000716 1000576 1000682 1001418
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## 1000910 1001786 1001474 1000742 1001554 1001511 1000246 1001551 1001263
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## 1001374 1001768 1000632 1001171 1000706 1001862 1000253 1001471 1000856
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## 1000841 1000473 1001362 1001186 1001796 1000187 1001332 1000200 1001392
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## 1000279 1000938 1001681 1001557 1000616 1000603 1001750 1000908 1001727
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## 1001326 1001519 1001669 1001515 1001823 1000993 1001715 1000962 1001827
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## 1000010 1000963 1001606 1000866 1000739 1001663 1000907 1001891 1000177
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## 1000375 1001195 1001884 1000659 1001135 1001247 1000660 1000942 1000393
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## 1001806 1001954 1000567 1001780 1000302 1001890 1000147 1001559 1000366
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## 1001305 1001060 1000967 1000457 1000516 1001042 1001788 1001311 1001749
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## 1001916 1001678 1000015 1000624 1001280 1000930 1000721 1001296 1000795
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## 1001345 1000356 1001881 1001728 1000148 1001411 1000255 1001490 1000515
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## [2,] 1 0 0 0 0 0 0 0 1
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## 1000419 1000755 1001717 1000662 1001777 1000170 1001835 1000956 1001931
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## 1001805 1000793 1001666 1000874 1001695 1000595 1000709 1001649 1000449
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## 1002033 1000569 1000227 1001092 1000690 1000927 1000653 1000237 1000883
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## 1001988 1001980 1000263 1002037 1001415 1002038 1000865 1001667 1001818
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## 1000547 1000946 1001725 1000301 1000208 1000902 1000670 1000361 1001839
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## 1001497 1001789 1001945 1000840 1001766 1001686 1000929 1000123 1000005
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## 1000974 1001629 1001654 1001922 1001203 1001918 1000122 1001096 1001033
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## 1001970 1001323 1000331 1001738 1000408 1001405 1000378 1001053 1001675
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## 1000691 1000340 1001809 1000353 1000583 1001908 1001683 1001888 1000808
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## 1001468 1001301 1000837 1000070 1000617 1000086 1001757 1001612 1001600
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## 1000994 1000625 1000259 1001933 1000007 1000623 1001160 1000875 1000664
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## 1001849 1000879 1000081 1000090 1000966 1000053 1001940 1001455 1000334
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## 1000786 1000461 1001702 1000825 1002016 1000134 1000945 1001220 1000678
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## 1000249 1000638 1000112 1001378 1000092 1001480 1001494 1001165 1000728
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## 1001755 1001760 1001737 1002031 1001286 1000059 1001433 1000506 1000323
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## 1000258 1000641 1000609 1001604 1000179 1000941 1000740 1001292 1001904
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## 1000685 1001787 1001664 1000688 1001237 1001898 1000997 1000651 1000950
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## 1001917 1001653 1001457 1000857 1000861 1000075 1001726 1001072 1001174
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## 1000247 1001578 1001754 1000403 1000376 1000178 1001928 1000088 1001333
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## 1001628 1000133 1000305 1001962 1000767 1001266 1000572 1000736 1001192
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## 1001315 1000271 1000557 1000398 1001746 1001698 1000102 1000365 1001212
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## 1001207 1000677 1001262 1001645 1001363 1001103 1002041 1001209 1001668
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## 1000477 1001844 1000848 1001380 1001486 1000896 1001348 1001943 1001030
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## 1001689 1000597 1001164 1001377 1001094 1000976 1001295 1001337 1001859
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## 1000971 1001187 1001069 1001079 1001769 1001895 1000047 1001581 1002017
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## [2,] 1 0 0 0 0 0 0 0 0
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## 1001685 1001597 1001521 1001491 1001113 1001218 1000414 1001438 1000291
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## [2,] 0 0 0 0 0 1 0 0 0
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## 1001894 1001977 1000726 1000151 1000438 1001327 1001044 1001419 1001566
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## 1000931 1001585 1001636 1001260 1000031 1001016 1000243 1000326 1000831
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001860 1000074 1001864 1001152 1001620 1001514 1001319 1000505 1000240
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## 1001500 1001855 1001071 1001882 1000573 1001276 1001997 1001172 1000922
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## 1000242 1000091 1001125 1000565 1001005 1000114 1001109 1000816 1001679
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001912 1001236 1000636 1000265 1001223 1000095 1000422 1001658 1000278
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001691 1000384 1001316 1000510 1001365 1001479 1000692 1000776 1000030
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
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## 1000934 1001887 1000654 1001505 1002019 1000437 1000754 1000232 1000630
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## [6,] 0 1 0 0 0 0 0 0 0
## 1001532 1001957 1000132 1001782 1001126 1001265 1001104 1000488 1001025
## [1,] 0 0 0 0 0 1 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 1 0 0 0 0 0 0 1
## 1001351 1000656 1001325 1001778 1001488 1000819 1001640 1001955 1001355
## [1,] 0 0 1 1 0 0 1 0 0
## [2,] 0 0 0 1 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000225 1001536 1000391 1000900 1000943 1001641 1001579 1000884 1000531
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 1 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 1 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001509 1001704 1001696 1000783 1000096 1000217 1000684 1001416 1001329
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000601 1000988 1000911 1001555 1001085 1001199 1002023 1000978 1000089
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 1 0 0 0 0 0 0
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## [5,] 0 1 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001530 1001989 1001427 1000708 1001711 1000293 1000377 1001011 1001056
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## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000149 1000284 1000899 1000715 1001226 1001035 1000499 1000045 1001240
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001495 1000117 1001393 1000439 1000995 1000903 1000634 1000381 1000979
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 1 0 0 0 0 0 0
## 1000738 1000078 1000703 1001886 1000520 1000524 1001369 1002018 1001285
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 1 0 1 0 0 0 0 0 0
## 1000514 1000143 1000718 1000533 1001960 1001403 1000120 1000383 1000871
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## [2,] 0 0 0 1 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## 1000711 1000121 1000341 1000098 1000989 1000424 1000661 1001364 1002042
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1001227 1000839 1000667 1001436 1000704 1000215 1002046 1001605 1000968
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001435 1000702 1001618 1000763 1001045 1000643 1001055 1001467 1001974
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## [2,] 0 0 0 0 0 0 0 0 0
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## 1000778 1001924 1000618 1000949 1001215 1000627 1001522 1000236 1001061
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 1 0 0 1 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000919 1000588 1001643 1000024 1000821 1000210 1001407 1001206 1000973
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## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000185 1000063 1001396 1001851 1000049 1000770 1001524 1000810 1001873
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## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## 1001776 1000136 1000083 1000626 1000764 1002047 1000782 1001049 1001170
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1002003 1002014 1000402 1000055 1001054 1000367 1001512 1002050 1001547
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## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001470 1000300 1001889 1000042 1000792 1000551 1000146 1001807 1000144
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 1 1 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000924 1002002
## [1,] 0 0
## [2,] 0 0
## [3,] 1 0
## [4,] 0 0
## [5,] 0 0
## [6,] 0 0head(Z2)## 1001562 1001362 1001488 1001115 1001465 1000803 1000542 1001438 1000519
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 1 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 1 0 0 0 0 0 0 0 0
## 1000275 1000661 1002003 1001247 1000478 1000958 1001050 1000874 1000970
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 1
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1001354 1001019 1000233 1001989 1000829 1001967 1000608 1001638 1000522
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 1 1
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000495 1000015 1001471 1000422 1001828 1001474 1001761 1000527 1001609
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001185 1001639 1001653 1000264 1001491 1001088 1000296 1000036 1000336
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000983 1001193 1000875 1001777 1001345 1001831 1001211 1000001 1001958
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
## [3,] 0 0 0 0 1 0 0 1 0
## [4,] 0 0 0 1 0 0 0 0 0
## [5,] 0 0 1 0 0 0 0 0 0
## [6,] 1 0 0 0 0 0 0 0 0
## 1000244 1000081 1001662 1000346 1000288 1001527 1000704 1001421 1001161
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 0 1 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 1 0
## [5,] 0 0 0 1 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000082 1001709 1000405 1000816 1001534 1000427 1001289 1000585 1000797
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 1 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1001599 1000459 1000698 1002037 1001036 1002030 1001720 1001523 1000031
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 1 0 0 0 0 0 0 0 0
## 1000387 1000128 1000988 1000537 1000968 1001694 1000523 1001315 1000281
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000058 1001970 1001622 1001868 1000136 1000391 1001695 1001203 1000345
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 1 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001033 1001068 1001282 1000656 1001448 1000525 1001903 1000457 1000021
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000945 1000411 1000666 1001644 1001990 1000292 1001439 1000256 1001208
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1000730 1000920 1000688 1000171 1001156 1001392 1001003 1001337 1000777
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001384 1000129 1000494 1001213 1001703 1001928 1000508 1001632 1000132
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 1 0 0 0
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## [5,] 0 0 1 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001946 1001081 1001080 1000682 1000728 1000220 1000550 1001382 1001045
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001204 1000179 1001199 1001357 1000750 1000407 1000813 1001667 1001025
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1000088 1000759 1001685 1001347 1001396 1001544 1001149 1001979 1000341
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0
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## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001611 1001058 1001974 1000972 1000701 1001824 1000080 1000365 1000578
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 0 0 0 0
## 1000756 1001108 1001689 1000454 1001768 1000062 1001490 1001222 1000312
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
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## [6,] 0 0 0 0 0 1 0 0 0
## 1000914 1001743 1001174 1001569 1000832 1001487 1001405 1000452 1000838
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
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## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000305 1001216 1000120 1000597 1001801 1000142 1001026 1001269 1000634
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 1 0 0 0 0 0 0 1
## [5,] 0 1 0 0 0 0 0 0 0
## [6,] 0 0 1 0 0 0 0 0 0
## 1000140 1000771 1000768 1000493 1000056 1002020 1000351 1000491 1001346
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 0 0 0 0 0 1
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## 1000301 1000762 1000106 1001916 1000349 1001128 1001913 1000153 1001735
## [1,] 0 0 0 0 0 0 0 0 0
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## 1001848 1000989 1000512 1001079 1001752 1000004 1001957 1001316 1000811
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## 1001900 1001969 1000450 1001173 1001129 1000022 1000187 1000818 1000959
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## 1001578 1001434 1000173 1000064 1001376 1000419 1000907 1000721 1000089
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## 1000190 1000526 1000680 1001751 1000073 1001939 1001770 1001287 1001531
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## 1000334 1000318 1001400 1001769 1001084 1000261 1001721 1000145 1000402
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## 1000735 1001859 1002049 1001505 1000582 1000779 1000394 1001116 1000484
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## 1001228 1000830 1000996 1000054 1001302 1001546 1001221 1000609 1000151
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## 1000889 1000979 1000555 1000163 1001941 1001494 1001509 1001563 1000513
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## 1001444 1000540 1001243 1000781 1000333 1000581 1001132 1000018 1000497
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## 1002014 1001702 1001839 1000827 1000279 1000935 1000743 1001986 1000998
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## 1000029 1000302 1000700 1001972 1001201 1000568 1001331 1002048 1001147
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## 1001782 1001637 1000869 1001038 1000971 1000092 1001592 1001236 1001602
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## 1000388 1000804 1000819 1001549 1001608 1000241 1000099 1001547 1000904
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## 1000074 1001106 1000776 1001516 1000168 1001895 1001412 1000378 1000510
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## 1001136 1000020 1001458 1000409 1000865 1000447 1000461 1000699 1001191
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## 1000891 1000913 1000717 1001909 1000446 1001672 1000726 1000901 1001283
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## 1001786 1001428 1002044 1001603 1001835 1001235 1000048 1001010 1000480
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## 1001329 1000671 1000050 1000664 1001552 1002031 1001805 1000985 1000211
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## 1000316 1000658 1000576 1001870 1001593 1000793 1001518 1001798 1001696
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## 1000060 1000259 1001788 1001885 1000623 1000118 1001120 1001767 1000628
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## 1000306 1001078 1001520 1000744 1000932 1001197 1000853 1001395 1000919
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## 1000580 1000040 1001844 1000760 1000290 1000766 1001591 1000780 1000859
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## 1000645 1000487 1002009 1000596 1000903 1001894 1001849 1000636 1000131
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## 1001661 1000751 1001610 1001998 1001953 1000549 1002021 1001367 1001882
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## 1000130 1000135 1000898 1000167 1001364 1001485 1001650 1000071 1001822
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## 1001398 1001431 1001692 1000967 1000201 1000724 1002011 1000185 1002010
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## 1000158 1001313 1001556 1001083 1001065 1001816 1001260 1000675 1001607
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## 1001048 1000321 1001737 1001432 1002015 1001095 1000277 1000270 1001455
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## 1000976 1000038 1000507 1002016 1001765 1000413 1001815 1000295 1001875
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## 1001543 1000554 1000424 1000844 1000395 1001386 1000561 1001734 1001620
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## 1000052 1000588 1000340 1000836 1001164 1001290 1000651 1000107 1001980
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## 1001171 1002001 1000225 1001820 1000150 1000980 1000882 1001567 1001368
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## 1001956 1000878 1001255 1000209 1001864 1000591 1000560 1001677 1000809
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## 1000641 1000355 1001349 1001522 1001511 1000331 1001526 1000753 1000339
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## 1001375 1000727 1000458 1001324 1001837 1001933 1000222 1000079 1001373
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## 1000855 1001322 1000285 1000093 1001597 1001284 1002047 1001427 1000192
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## 1000437 1001792 1001524 1000617 1001175 1001234 1000087 1001326 1001005
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## 1001319 1000625 1001138 1000631 1001730 1000668 1001915 1001154 1000745
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## 1001754 1000403 1001478 1001936 1000587 1001409 1001983 1000856 1000978
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## 1001759 1000243 1001336 1001726 1001372 1000611 1001823 1001477 1001032
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## 1000821 1001766 1000398 1001647 1000096 1000377 1000483 1000613 1000624
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## 1000725 1001833 1001564 1001214 1000481 1000817 1001303 1001881 1000614
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## 1001107 1000032 1001385 1001253 1001144 1000546 1001714 1000234 1000747
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## 1001142 1000194 1000329 1000178 1001797 1001446 1001393 1001024 1000693
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## 1001846 1000607 1001397 1000667 1001259 1001570 1000146 1001555 1001422
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## 1001486 1000548 1001229 1001196 1000964 1000551 1000772 1001584 1001381
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## 1000051 1001879 1000547 1001186 1001981 1000169 1001907 1001454 1000977
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## 1001122 1000991 1001168 1000154 1000925 1001210 1000381 1000278 1000294
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## 1001919 1000470 1001812 1001441 1000595 1000436 1001968 1000144 1000266
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## 1000687 1000367 1000937 1001297 1001425 1000660 1000815 1000620 1001343
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## 1000024 1000674 1000404 1002046 1000533 1001691 1001139 1001942 1000738
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## 1000590 1001015 1001832 1000849 1001497 1001351 1001300 1000215 1000026
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## 1000705 1001037 1000951 1000440 1000795 1001890 1001449 1000260 1000061
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## 1000247 1001899 1000798 1001744 1001311 1000647 1001043 1001371 1001325
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## 1001854 1000303 1000276 1000637 1000742 1000782 1001039 1000297 1001557
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## 1000536 1000172 1000683 1001717 1001802 1000558 1000794 1000752 1000702
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## 1001654 1001224 1000820 1001641 1000720 1000039 1001074 1001082 1001157
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## 1001627 1000933 1001320 1000028 1000226 1000203 1000629 1000670 1001334
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## 1001932 1000562 1000240 1001795 1000134 1000423 1000396 1001077 1000566
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## 1001648 1000858 1000412 1001369 1000888 1001342 1001151 1001718 1000085
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## 1001806 1001198 1001594 1000148 1000600 1000070 1000108 1001338 1000224
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## 1000605 1001131 1001500 1001757 1001582 1000999 1001588 1001237 1000784
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## 1000642 1001099 1000152 1000267 1000067 1000924 1000592 1001030 1000498
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## 1001124 1001103 1001090 1001748 1002033 1001572 1001059 1000765 1000221
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## [4,] 0 0 1 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 1 0 0 0 0 0 0 0 0
## 1001503 1001062 1000679 1001126 1000110 1000006 1000475 1001445 1000390
## [1,] 0 0 0 0 0 0 1 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1002004 1000563 1000444 1001966 1000095 1000638 1000886 1000471 1001220
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 1 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 1 0 0 0
## 1001391 1001938 1000974 1000121 1000757 1000517 1000800 1001271 1001181
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 1 0 0 0 0 0 0 0 0
## 1001924 1001809 1001857 1001679 1001728 1001878 1000307 1001568 1000327
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001109 1000075 1000543 1000210 1001698 1001982 1000622 1000111 1001013
## [1,] 0 0 0 0 0 0 0 1 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 0 0 0 0 0
## [5,] 0 0 0 0 1 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001910 1001469 1000692 1001353 1000343 1001521 1000499 1000466 1001293
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 1 0 0 0 0 0 0 0
## 1002000 1000627 1000887 1001763 1001447 1000098 1000506 1000939 1001361
## [1,] 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 1
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000283 1000069 1000577 1001162 1001955 1000948 1000962 1000250 1001533
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000428 1000847 1001604 1001540 1000477 1001678 1001426 1001736 1000769
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 1 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000196 1000474 1000824 1001621 1001749 1000401 1000492 1000137 1000599
## [1,] 0 0 1 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 1 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001952 1002028 1001459 1001755 1000556 1001146 1001098 1001194 1000496
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 1 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1001794 1001529 1000160 1000286 1001360 1000737 1000557 1000149 1000938
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000023 1000872 1001771 1000615 1001937 1001451 1000265 1000736 1000025
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001223 1000956 1001484 1001002 1000468 1001758 1001339 1000695 1000012
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001585 1000467 1001092 1000076 1000010 1002019 1000503 1000166 1000042
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000734 1000703 1001104 1000170 1000269 1001537 1000335 1000202 1001163
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000354 1000078 1000366 1001711 1000383 1001962 1000359 1001066 1001973
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000876 1000420 1000490 1002006 1000033 1001442 1001510 1001629 1001940
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001681 1000369 1000007 1001908 1001954 1001646 1000337 1000479 1000005
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 1 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000003 1001496 1001830 1001595 1002029 1000770 1001921 1001021 1001845
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000298 1000544 1000035 1001862 1000181 1001676 1002034 1001318 1000987
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1002017 1000571 1001017 1001616 1001821 1001244 1001472 1001893 1000570
## [1,] 0 0 0 1 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000094 1001866 1000612 1001052 1001643 1001105 1001606 1000944 1001054
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 1 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000799 1001215 1001009 1000719 1000706 1000626 1000940 1001976 1000330
## [1,] 0 1 1 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1001538 1000729 1001443 1000864 1001614 1000251 1000686 1000616 1001328
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001664 1000322 1000072 1001261 1000104 1002013 1001612 1001167 1002035
## [1,] 0 0 0 0 1 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 1 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000184 1000463 1000949 1000460 1001542 1001452 1001590 1000375 1001876
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 0 0 1 0 0 0 1 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001380 1000541 1000993 1000255 1001404 1000632 1000633 1001027 1001246
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000814 1001498 1002005 1001574 1001348 1001305 1001508 1000352 1000236
## [1,] 0 0 0 0 1 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001541 1001961 1001840 1001814 1001075 1001148 1000103 1000530 1000767
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 1 0 0 0 0 0 0 0
## 1002042 1000758 1000565 1001202 1001581 1000464 1001281 1002025 1002002
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001834 1000013 1000761 1001577 1001930 1000324 1000254 1001067 1000505
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 1 0 1 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000610 1001551 1000238 1001183 1001841 1000253 1001123 1000268 1001501
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 1 0 0 0 0 0
## [4,] 0 0 0 0 0 1 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001172 1000982 1001649 1001775 1000162 1000373 1000347 1001410 1000176
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 1 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001732 1000049 1001279 1001309 1000604 1000787 1000713 1001950 1001829
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 1
## [3,] 0 0 0 0 0 0 0 1 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000807 1001180 1001061 1000027 1000969 1000282 1000309 1001615 1000084
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 1 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1002027 1000252 1001209 1001668 1001056 1000696 1001559 1001863 1001724
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001435 1001254 1001263 1001550 1001741 1001660 1001819 1000586 1000193
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 1 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001429 1000514 1000257 1001121 1000101 1000328 1002023 1000535 1001657
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 1 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1000619 1000434 1000183 1001850 1001975 1001927 1000603 1000147 1000348
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 1
## [6,] 0 1 0 0 1 0 1 0 0
## 1000851 1001912 1001100 1001799 1000141 1000314 1000846 1000922 1000741
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1001513 1000621 1001633 1000975 1000690 1001704 1001262 1000908 1000207
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001418 1001750 1000364 1001133 1001169 1001073 1001545 1001712 1000358
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000918 1001791 1000835 1000862 1001249 1001877 1000802 1001926 1000159
## [1,] 0 0 0 0 0 0 0 0 1
## [2,] 0 1 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000441 1001565 1000952 1001327 1001873 1001276 1000928 1001793 1001394
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 1 0 0 0 0 0
## 1000892 1001723 1000155 1001669 1000926 1000973 1000950 1000841 1000102
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 1 0 0 0 0
## 1000961 1001947 1000304 1001227 1000733 1000112 1001719 1000415 1002050
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001365 1000037 1000676 1001871 1000125 1000399 1001701 1001554 1000654
## [1,] 0 0 1 0 0 0 1 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 1
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000689 1001330 1000272 1000342 1000994 1000397 1000644 1001963 1000091
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001004 1000291 1001535 1000553 1001887 1000489 1000837 1001200 1001856
## [1,] 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 1 0 0 0 0
## [3,] 0 1 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 1 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001238 1001323 1000311 1001515 1001218 1001827 1000755 1001022 1000902
## [1,] 0 0 1 0 1 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000117 1000618 1000785 1001589 1001984 1001127 1001773 1001401 1001715
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001308 1000188 1000572 1000746 1001625 1000893 1001264 1000681 1001402
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001457 1000219 1000796 1000180 1000946 1000929 1000791 1000338 1000284
## [1,] 0 0 1 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 1 0 0 0 0
## [5,] 0 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000931 1000191 1002045 1001093 1000115 1001335 1000863 1000916 1000156
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 1 0 0 0 0 0 0 0 0
## [4,] 0 0 0 1 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000432 1001306 1001414 1001504 1001598 1001923 1000485 1001959 1000790
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 1 0 0
## [6,] 0 0 0 0 0 0 0 0 1
## 1000198 1000157 1001675 1000635 1000353 1001507 1001911 1001240 1001314
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001925 1000810 1001920 1000386 1000034 1000456 1001600 1001628 1001378
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 1 0 0 0 0 1 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001097 1001159 1001756 1000231 1001631 1001796 1001278 1000287 1001207
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 1 0 0 0 0
## 1001055 1001089 1000511 1001072 1000639 1001028 1000665 1001733 1000652
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 1 1 0 1
## [6,] 0 0 0 0 0 0 0 0 0
## 1001645 1001618 1001299 1001179 1001420 1001810 1000242 1000195 1001411
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 1 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000500 1001560 1001470 1001778 1001020 1001964 1000539 1000164 1000593
## [1,] 0 0 0 0 0 0 0 1 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 1 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1001663 1000806 1000389 1001460 1001063 1001195 1000900 1001433 1000715
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000659 1001781 1001285 1000433 1001206 1001707 1001188 1002026 1001064
## [1,] 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 1 0
## [6,] 0 0 0 0 0 0 0 0 0
## 1000473 1000083
## [1,] 0 0
## [2,] 0 0
## [3,] 0 0
## [4,] 0 0
## [5,] 0 0
## [6,] 0 0head(pheno1)## y sex bmi ybin time status
## 1 -0.6726497 1 25.30159 1 7 1
## 2 0.2171797 2 22.80376 1 9 1
## 3 0.4867783 1 23.83211 0 9 0
## 4 0.3465593 2 27.09918 1 4 1
## 5 -0.9432163 1 21.43145 1 5 1
## 6 0.9721536 2 25.69850 0 7 1head(pheno2)## id y sex bmi
## 10001 10001 -0.68009794 1 24.49436
## 10002 10002 1.04832618 2 22.86157
## 10003 10003 0.04356970 1 27.14200
## 10004 10004 -0.30263426 2 23.90935
## 10005 10005 0.01489937 1 29.21902
## 10006 10006 -1.86419978 2 22.84718head(SNPInfo)## Name gene
## 1 1000001 gene1
## 2 1000002 gene1
## 3 1000003 gene1
## 4 1000004 gene1
## 5 1000005 gene1
## 6 1000006 gene1Perform the burden test that finds genes that contain rare variants that can explain dependent variable y in the two cohorts.
cohort1 <- prepScores(Z=Z1, y~1, SNPInfo=SNPInfo, data=pheno1)
cohort2 <- prepScores(Z=Z2, y~1, SNPInfo=SNPInfo, data=pheno2)
out <- burdenMeta(cohort1, cohort2, SNPInfo = SNPInfo, mafRange=c(0, 0.01))
out$p## [1] 0.804564814 0.046161104 NA NA NA 0.263407302
## [7] NA 0.918255314 NA NA 0.811254045 0.970457899
## [13] 0.004559151 0.131274688 0.722047247 0.766267154 NA NA
## [19] 0.213399304 0.599477839 0.492742980 NA 0.150989236 NA
## [25] 0.400078883 0.337728462 NA 0.106348500 0.678144245 NA
## [31] NA NA 0.128288013 0.982241458 0.673502993 0.333450136
## [37] NA 0.662150090 0.257418803 0.516930816 NA NA
## [43] 0.594097026 0.702123102 0.941726367 0.641861505 0.522236741 0.943271738
## [49] NA NA NA NA NA NA
## [55] 0.744218473 0.501080548 0.364138688 0.857083065 0.659642815 0.716943249
## [61] NA 0.691089146 0.401763495 0.274840325 NA NA
## [67] NA 0.807759418 NA NA 0.839965079 0.066783508
## [73] NA NA 0.417362536 0.600727311 NA NA
## [79] NA 0.971857104 NA NA 0.183859126 NA
## [85] NA 0.922685493 NA 0.662012460 NA 0.484152859
## [91] 0.318236576 NA NA NA NA NA
## [97] 0.949230030 0.345079969 0.203656236 0.897861513burdenMeta() function provided by seqMeta library provides burden test that is based on a linear regression model. The internal computation involves getting the linear regression model lm(y ~ burden + group) when burden is the number of rare variants that exists in a gene of interest in the sample, and from that getting p-value. So burden test is a good way to detecting causal variants of a phenotype if the variants in that region have same directionality in causality with the phenotype.
So as variations of burden test, Combined Multivariate and Collapsing method (CMC); Li and Leal, 2008 and Cohort Allelic Sums Test (CAST); Morgenthaler and Thilly, 2007, etc. exist.
2-2. Single Variant Burden Test Using EPACTS (Efficient and Parallelizable Association Container Toolbox)
EPACTS (Efficient and Parallelizable Association Container Toolbox) is an anlytical tool that supports single nucleotide variant-level burden tests as well as gene-perspective and case-perspective burden tests.
It uses VCF files that contain the genomic variations and PED files that contain phenotype with pedigree information. The threshold for rare variant is set at less than MAF 1% with --min-maf argument. The input VCF file is --vcf 1000G_exome_chr20_example_softFiltered.calls.vcf.gz that contains chromosome 20 of 1000 genomes project’s information. The input PED file is --ped 1000G_dummy_pheno.ped.
[soh1@x020 chapter6]$ cd RareVariant
[soh1@x020 RareVariant]$ ls
data out plot snp2hla vcftabix -p vcf data/1000G_exome_chr20_example_softFiltered.calls.vcf.gzWe need EPACTS before proceeding, so download the latest version from EPACTS github at https://github.com/statgen/EPACTS through git and install. This is so called “clone the repo and build it” command.
[soh1@x020 RareVariant]$ git clone https://github.com/statgen/EPACTS
Cloning into 'EPACTS'...
remote: Enumerating objects: 1449, done.
remote: Total 1449 (delta 0), reused 0 (delta 0), pack-reused 1449
Receiving objects: 100% (1449/1449), 172.57 MiB | 15.60 MiB/s, done.
Resolving deltas: 100% (563/563), done.
Checking out files: 100% (518/518), done.gda@GDA： 〜/RareVariant$ epacts single —-vcf data/1000G_exome_chr20_example_softFiltered.calls.vcf.gz ——ped data/1000G_dummy_pheno.ped --min-mat 0.001 --chr 20 --pheno DISEASE --cov AGE --cov SEX --test b.score --anno --out out/test.single.b.score --run 2This results in top 5000 association study results and performs quantile-quantile graph and Manhattan graph analysis per MAF.
zcat out/test.single.b.score.epacts.gz | headhead out/test.single.b.score.epacts.top5000The resulting file contains following contents:
- NS: Number of Phenotype Samples with that Genotype
- AC: Number of Total Reference Alternative Alleles
- CALLRATE: Rate of non-missing genotypes called successfully
- MAF: Minor Allele Frequency
- PVALUE: p-value of Single Nucleotide Variant test
- AF.CASE: Allele frequency of experimental group variants
- AF.CTRL: Allele frequency of control group variants
epacts anno --in data/1000G_exome_chr20_example_softFiltered.calls.vcf.gz --out data/1000G_exome_chr20_example_sfotFiltered.calls.anno.vcf.gzepacts group --vcf data/1000G_exome_chr20_example_softFiltered.calls.anno.vcf.gz --groupf data/1000G_exome_chr20_exapmle_softFiltered.calls.anno.grp --out out/test.gene.skat --ped data/100G_dummy_pheno.ped --max-maf 0.05 --sepchr 20 --pheno QT --cov AGE --cov SEX --test skat --skat-o --run 2So, apparently SKAT is a test for association between a set of rare (and common) variant and continuous/dichotomous phenotypes using kernel machine methods. Here’s the homepage.
- NS: Phenotype sample number that has such genotypes
- FRAC_WITH_RARE: Fraction of individuals with rare variants
- NUM_ALL_VARS: number of variants that defines a group
- NUM_PASS_VARS: –min-maf, –min-mac, –max-maf, –min-callrate. Number of variants containing these thresholds
- NUM_SING_VARS: Number of singletons that correspond to variants in NUM_PASS_VARS.
- PVALUE: P-value of burden test
2-3. SKAT Association Study
Apply SKAT (Sequence Kernel Association Test) to the same seqMetaExample dataset. SKAT uses distribution elements of random effect model.
cohort1 <- prepScores(Z=Z1, y~sex+bmi, SNPInfo = SNPInfo, data=pheno1)
cohort2 <- prepScores(Z=Z2, y~sex+bmi, SNPInfo = SNPInfo, kins=kins, data=pheno2)
out.skat <- skatMeta(cohort1, cohort2, SNPInfo=SNPInfo)
out.skat[order(out.skat$p), ]
SNPInfo variable contains in which genes each variant is contained.
We use sex and bmi variables as covariates to perform SKAT test. Even in Burden test you can designate covariates if you write y~sex+bmi instead of y~1. SKAT method calculates the score of specific gene or region by considering how variants are distributed. Therefore, unlike burden test, it can catch signal even if the variants are not oriented towards particular directionality in causality. Genes gene98, gene28, etc. explain the dependent variable y well and these are the significant rare variant genes associated with rare diseases.
2-3. SKAT-O Association Study
SKAT-O uses advantages of both burden test and SKAT to optimize statistical power. SKAT-O’s O means ‘optimal’ and it corrects for type-I errors that occur when sample size is small. Usage is same as SKAT, and you use skatOMeta() instead of skatMeta().
out.skat <- skatOMeta(cohort1, cohort2, SNPInfo = SNPInfo)
out.skat[order(out.skat$p), ]3. Linkage Disequilibrium Data Analysis
Let’s calculate LD from publicly available data that is from 1000 genomes project. We use VCF of 104 JPT people’s data but if you’ve got enough time, it’s better for you to calculate LD from many more data like EAS 504. We check if we’ve got the necessary files. The VCF file has already been extracted with variants between position of chr16:54000000-54050000.
[soh1@x020 RareVariant]$ ls
data EPACTS out plot snp2hla vcf
[soh1@x020 RareVariant]$ cd vcf
[soh1@x020 vcf]$ ls
JPT_part.vcf.gz JPT_part.vcf.gz.tbi3-1. PED/MEP file formats
Let’s talk about PLINK input format. First of all, we’ve got *.PED (BED) that contains pedigree, genotype, and phenotype data. So we have total of 6 + 208 columns,
- Column 1 = Family ID
- Column 2 = Individual ID
- Column 3 = Paternal ID (when it’s 0, missing)
- Column 4 = Mataernal ID (when it’s 0, missing)
- Ciolumn 5 = Sex
- Column 6 = Phenotype (1, 2, or 0; 1 = unaffected, 2= affected, 0 = missing)
- Columns 7 + 8 = Genotype pair of SNP1 (missing if 0)
- Columns 9 + 10 = Genotype pair of SNP2 (missing if 0)
Now, *.MAP file contains the variant information of each.
- Column 1 = chromosome number
- Column 2 = SNP ID
- Column 3 = Genetic Distance (morgans)
- Column 4 = physical base-pair position (bp)
The two files have relationship as described below.
3-2. Convert from VCF to PED
[soh1@x020 vcf]$ vcftools --gzvcf JPT_part.vcf.gz --plink-tped --out JPT --phased
VCFtools - v0.1.12b
(C) Adam Auton and Anthony Marcketta 2009
Parameters as interpreted:
--gzvcf JPT_part.vcf.gz
--out JPT
--phased
--plink-tped
Using zlib version: 1.2.3
Versions of zlib >= 1.2.4 will be *much* faster when reading zipped VCF files.
After filtering, kept 104 out of 104 Individuals
Writing PLINK TPED file ... PLINK-TPED: Only outputting biallelic loci.
Writing PLINK TFAM file ... Done.
After filtering, kept 1388 out of a possible 1388 Sites
Run Time = 0.00 seconds
[soh1@x020 vcf]$ ls
JPT.log JPT_part.vcf.gz JPT_part.vcf.gz.tbi JPT.tfam JPT.tpedYou can see that there are resulting ouput files (*.log, *.tped, *.tfam). The very first four columns in the *.tped file contains variant information and the 208 columns that follow contain alleles of 104 people. Each of the pairs of bases cut sequentially represent one person’s genotype. *.tfam file represents one person per one row, and contains information about individuals and families. Each of the six columns mean Family ID, Individual ID, Paternal ID, Maternal ID, Sex (1=male, 2=female, other=unknown), Phenotype.
[soh1@x020 vcf]$ more JPT.tped
16 rs150805752 0 54000022 C C C C C C C C C C C C C C C C C C C C CC
16 rs139198525 0 54000023 G G G G G G G G G G G G G G G G G G G G GG
16 16:54000027 0 54000027 A A A A A A A A A A A A A A A A A A A A AA
16 16:54000078 0 54000078 T T T T T T T T T T T T T T T T T T T T TT
16 16:54000108 0 54000108 T T T T T T T T T T T T T T T T T T T T TT
16 rs143690163 0 54000121 C C C C C C C C C C C C C C C C C C C C C
--More--(0%)[soh1@x020 vcf]$ more JPT.tfam
EAS_JPT_NA18939_F EAS_JPT_NA18939_F 0 0 0 0
EAS_JPT_NA18940_M EAS_JPT_NA18940_M 0 0 0 0
EAS_JPT_NA18941_F EAS_JPT_NA18941_F 0 0 0 0
EAS_JPT_NA18942_F EAS_JPT_NA18942_F 0 0 0 0
EAS_JPT_NA18943_M EAS_JPT_NA18943_M 0 0 0 0
EAS_JPT_NA18944_M EAS_JPT_NA18944_M 0 0 0 0
EAS_JPT_NA18945_M EAS_JPT_NA18945_M 0 0 0 0
EAS_JPT_NA18946_F EAS_JPT_NA18946_F 0 0 0 0
EAS_JPT_NA18947_F EAS_JPT_NA18947_F 0 0 0 0
EAS_JPT_NA18948_M EAS_JPT_NA18948_M 0 0 0 0
EAS_JPT_NA18949_F EAS_JPT_NA18949_F 0 0 0 0
EAS_JPT_NA18950_F EAS_JPT_NA18950_F 0 0 0 0
EAS_JPT_NA18951_F EAS_JPT_NA18951_F 0 0 0 0
EAS_JPT_NA18952_M EAS_JPT_NA18952_M 0 0 0 0
EAS_JPT_NA18953_M EAS_JPT_NA18953_M 0 0 0 0
EAS_JPT_NA18954_F EAS_JPT_NA18954_F 0 0 0 0
EAS_JPT_NA18956_F EAS_JPT_NA18956_F 0 0 0 0
EAS_JPT_NA18957_F EAS_JPT_NA18957_F 0 0 0 0
EAS_JPT_NA18959_M EAS_JPT_NA18959_M 0 0 0 0
EAS_JPT_NA18960_M EAS_JPT_NA18960_M 0 0 0 0
EAS_JPT_NA18961_M EAS_JPT_NA18961_M 0 0 0 0
EAS_JPT_NA18962_M EAS_JPT_NA18962_M 0 0 0 0
EAS_JPT_NA18963_F EAS_JPT_NA18963_F 0 0 0 0
EAS_JPT_NA18964_F EAS_JPT_NA18964_F 0 0 0 0
EAS_JPT_NA18965_M EAS_JPT_NA18965_M 0 0 0 0
EAS_JPT_NA18966_M EAS_JPT_NA18966_M 0 0 0 0
EAS_JPT_NA18967_M EAS_JPT_NA18967_M 0 0 0 0
EAS_JPT_NA18968_F EAS_JPT_NA18968_F 0 0 0 0
EAS_JPT_NA18969_F EAS_JPT_NA18969_F 0 0 0 0
EAS_JPT_NA18970_M EAS_JPT_NA18970_M 0 0 0 0
EAS_JPT_NA18971_M EAS_JPT_NA18971_M 0 0 0 0
EAS_JPT_NA18972_F EAS_JPT_NA18972_F 0 0 0 0
--More--(30%)I downloaded plink binary executable from plink download page, named plink-1.07-x86_64.zip v1.07.
And unzipped the binary file with,
unzip plink-1.07-x86_64.
Then
[soh1@x020 vcf]$ ls
JPT.log JPT_part.vcf.gz JPT_part.vcf.gz.tbi JPT.tfam JPT.tped plink-1.07-x86_64Then I executed plink, giving arguments about –tped, –tfam, –make-bed, –out, and especially –noweb that tells plink not to go online to check for the latest version of plink.
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --tped JPT.tped --tfam JPT.tfam --make-bed --out ./JPT --noweb
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ ./JPT.log ]
Analysis started: Fri Aug 28 13:26:46 2020
Options in effect:
--tped JPT.tped
--tfam JPT.tfam
--make-bed
--out ./JPT
--noweb
** For gPLINK compatibility, do not use '.' in --out **
Reading pedigree information from [ JPT.tfam ]
104 individuals read from [ JPT.tfam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
Writing list of these individuals to [ ./JPT.nosex ]
1380 (of 1380) markers to be included from [ JPT.tped ]
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
Writing pedigree information to [ ./JPT.fam ]
Writing map (extended format) information to [ ./JPT.bim ]
Writing genotype bitfile to [ ./JPT.bed ]
Using (default) SNP-major mode
Analysis finished: Fri Aug 28 13:26:46 2020No we get binary BED, BIM, FAM files as output files. JPT.bed file’s column corresponds to an SNP, first four columns are SNPs, and 208columns are alleles.
JPT.bed file is a binary file with genotypes in it, so we can’t read it directly. JPT.bim contains alternative allele names and it’s an extended MAP file.
ALL.chr16.JPT.fam file, like ped file, has 6 columns (Family ID, Individual ID, Paternal ID, Maternal ID, Sex, Phenotype). JPT.nosex file contains two columns, which are Family ID and Individual ID.
[soh1@x020 vcf]$ more JPT.bim
16 rs150805752 0 54000022 0 C
16 rs139198525 0 54000023 0 G
16 16:54000027 0 54000027 0 A
16 16:54000078 0 54000078 0 T
16 16:54000108 0 54000108 0 T
16 rs143690163 0 54000121 0 C
16 16:54000185 0 54000185 0 G
16 rs373699250 0 54000190 0 T
16 rs147458024 0 54000198 T C
16 rs139841196 0 54000220 0 A
16 16:54000243 0 54000243 0 T
16 rs145462994 0 54000261 T A
16 16:54000380 0 54000380 0 C
16 rs147689010 0 54000381 0 A
16 16:54000430 0 54000430 0 T
16 16:54000521 0 54000521 0 G
16 rs7199210 0 54000588 0 A
16 rs148777468 0 54000672 0 G
16 16:54000765 0 54000765 0 C
16 16:54000772 0 54000772 0 C
16 rs73614162 0 54000773 0 G
16 rs1344502 0 54000792 G A
16 16:54000858 0 54000858 0 G
16 16:54000889 0 54000889 0 G
16 rs190638462 0 54000900 0 G
16 rs1111483 0 54000907 C A
16 16:54000953 0 54000953 0 G
16 rs181596393 0 54001000 0 G
16 16:54001001 0 54001001 0 C
16 16:54001005 0 54001005 0 G
16 16:54001010 0 54001010 0 G
16 rs186152990 0 54001028 0 G
--More--(2%)[soh1@x020 vcf]$ head JPT.fam
EAS_JPT_NA18939_F EAS_JPT_NA18939_F 0 0 0 -9
EAS_JPT_NA18940_M EAS_JPT_NA18940_M 0 0 0 -9
EAS_JPT_NA18941_F EAS_JPT_NA18941_F 0 0 0 -9
EAS_JPT_NA18942_F EAS_JPT_NA18942_F 0 0 0 -9
EAS_JPT_NA18943_M EAS_JPT_NA18943_M 0 0 0 -9
EAS_JPT_NA18944_M EAS_JPT_NA18944_M 0 0 0 -9
EAS_JPT_NA18945_M EAS_JPT_NA18945_M 0 0 0 -9
EAS_JPT_NA18946_F EAS_JPT_NA18946_F 0 0 0 -9
EAS_JPT_NA18947_F EAS_JPT_NA18947_F 0 0 0 -9
EAS_JPT_NA18948_M EAS_JPT_NA18948_M 0 0 0 -9[soh1@x020 vcf]$ head JPT.nosex
EAS_JPT_NA18939_F EAS_JPT_NA18939_F
EAS_JPT_NA18940_M EAS_JPT_NA18940_M
EAS_JPT_NA18941_F EAS_JPT_NA18941_F
EAS_JPT_NA18942_F EAS_JPT_NA18942_F
EAS_JPT_NA18943_M EAS_JPT_NA18943_M
EAS_JPT_NA18944_M EAS_JPT_NA18944_M
EAS_JPT_NA18945_M EAS_JPT_NA18945_M
EAS_JPT_NA18946_F EAS_JPT_NA18946_F
EAS_JPT_NA18947_F EAS_JPT_NA18947_F
EAS_JPT_NA18948_M EAS_JPT_NA18948_M3-3. Calculating Linkage Disequilibrium
Now calculate the LD relationship between SNPs rs11646260 and rs59578934.
--noweb: block web connection and run on local --bfile: get the binary file generated in the previous step --ld: prints the LD relationship calculated between two SNPs
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --noweb --bfile JPT --ld rs11646260 rs59578934
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ plink.log ]
Analysis started: Fri Aug 28 13:40:20 2020
Options in effect:
--noweb
--bfile JPT
--ld rs11646260 rs59578934
Reading map (extended format) from [ JPT.bim ]
1380 markers to be included from [ JPT.bim ]
Reading pedigree information from [ JPT.fam ]
104 individuals read from [ JPT.fam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
These individuals will be set to missing ( or use --allow-no-sex )
Writing list of these individuals to [ plink.nosex ]
Reading genotype bitfile from [ JPT.bed ]
Detected that binary PED file is v1.00 SNP-major mode
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
LD information for SNP pair [ rs11646260 rs59578934 ]
R-sq = 0.015 D' = 0.998
Haplotype Frequency Expectation under LE
--------- --------- --------------------
GC 0.014 0.007
AC 0.000 0.007
GT 0.471 0.479
AT 0.514 0.507
In phase alleles are GC/AT
Analysis finished: Fri Aug 28 13:40:20 2020So if you look at the section where it begins to say “LD information for SNP pair”, GC/AT are predicted as in phase alleles.
Now do the same for different positions.
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --noweb --bfile JPT --ld rs11646260 rs8063575
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ plink.log ]
Analysis started: Fri Aug 28 13:45:46 2020
Options in effect:
--noweb
--bfile JPT
--ld rs11646260 rs8063575
Reading map (extended format) from [ JPT.bim ]
1380 markers to be included from [ JPT.bim ]
Reading pedigree information from [ JPT.fam ]
104 individuals read from [ JPT.fam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
These individuals will be set to missing ( or use --allow-no-sex )
Writing list of these individuals to [ plink.nosex ]
Reading genotype bitfile from [ JPT.bed ]
Detected that binary PED file is v1.00 SNP-major mode
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
LD information for SNP pair [ rs11646260 rs8063575 ]
R-sq = 0.943 D' = 0.980
Haplotype Frequency Expectation under LE
--------- --------- --------------------
GG 0.481 0.238
AG 0.010 0.252
GA 0.005 0.247
AA 0.505 0.262
In phase alleles are GG/AA
Analysis finished: Fri Aug 28 13:45:46 2020R-sq value is the LD index, it assumes SNPs that have the square of correlation coefficient that is bigger than a set value as the tag SNPs. It’s between 0 to 1 and 0 means complete linkage equilibrium and 1 means complete linkage disequilibrium. If it’s over 1/3, it’s usually called as a strong LD.
\(0 \textrm{(complete LE)}<1/3 \textrm{(cutoff for a pretty strong LD)}<\textrm{R-sq}<1 \textrm{(complete LD)}\)
D’ value is also an LD index. If it’s equal to 1, it’s complete LD, if it’s equal to 0, then it’s complete LE. If it’s less than 1, somewhere along the previous generations there were genetic recombinations.
\(0 \textrm{(complete LE)}<\textrm{D'}\textrm{(Gene recombination occurred somewhere in previous generations)}<1 \textrm{(complete LD)}\)
Now compute LDs for all possible variant pairs along 54000000 to 54050000 bp in chromosome 16.
Usage Reminder:
- –bfile: get binary file from previous steps
- –chr: input chromosome position
- –from-bp: input the position of starting base
- –to-bp: input the position of end base
- –ld-snp: get the reference SNPs for LD computation
- –r2: calculate r2 value using the phased haplotypes
- –ld-window-r2: the r2 value used for filtering result
- –ld-window: the maximum number of SNPs between the SNPs used for calculating LD. the LD is for result filtering
- –ld-window-kb: maximum physical distance (in kb) between the SNPs used for calculating LD. the LD is for result filtering
[soh1@x020 vcf]$ ./plink-1.07-x86_64/plink --bfile JPT --chr 16 --from-bp 54000000 --to-bp 54050000 --ld-snp rs11646260 --r2 --ld-window-r2 0 --ld-window 999999 --ld-window-kb 99999 --noweb --out ./JPT
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ ./JPT.log ]
Analysis started: Fri Aug 28 14:01:28 2020
Options in effect:
--bfile JPT
--chr 16
--from-bp 54000000
--to-bp 54050000
--ld-snp rs11646260
--r2
--ld-window-r2 0
--ld-window 999999
--ld-window-kb 99999
--noweb
--out ./JPT
** For gPLINK compatibility, do not use '.' in --out **
Reading map (extended format) from [ JPT.bim ]
1380 markers to be included from [ JPT.bim ]
Scan region on chromosome 16 from [ rs150805752 ] to [ 16:54049880 ]
Reading pedigree information from [ JPT.fam ]
104 individuals read from [ JPT.fam ]
0 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 0 controls and 104 missing
0 males, 0 females, and 104 of unspecified sex
Warning, found 104 individuals with ambiguous sex codes
These individuals will be set to missing ( or use --allow-no-sex )
Writing list of these individuals to [ ./JPT.nosex ]
Reading genotype bitfile from [ JPT.bed ]
Detected that binary PED file is v1.00 SNP-major mode
*** WARNING *** DUPLICATE MARKERS FOUND ***
Duplicate marker name found: [ 16:54008614 ]
Before frequency and genotyping pruning, there are 1380 SNPs
104 founders and 0 non-founders found
Total genotyping rate in remaining individuals is 1
0 SNPs failed missingness test ( GENO > 1 )
0 SNPs failed frequency test ( MAF < 0 )
After frequency and genotyping pruning, there are 1380 SNPs
After filtering, 0 cases, 0 controls and 104 missing
After filtering, 0 males, 0 females, and 104 of unspecified sex
Writing LD statistics to [ ./JPT.ld ]
Analysis finished: Fri Aug 28 14:01:28 2020[soh1@x020 vcf]$ ls
JPT.bed JPT.fam JPT.log JPT_part.vcf.gz JPT.tfam plink-1.07-x86_64 plink.nosex
JPT.bim JPT.ld JPT.nosex JPT_part.vcf.gz.tbi JPT.tped plink.log[soh1@x020 vcf]$ head JPT.ld
CHR_A BP_A SNP_A CHR_B BP_B SNP_B R2
16 54032493 rs11646260 16 54000198 rs147458024 1.87066e-05
16 54032493 rs11646260 16 54000261 rs145462994 1.87066e-05
16 54032493 rs11646260 16 54000792 rs1344502 0.0213057
16 54032493 rs11646260 16 54000907 rs1111483 0.0213057
16 54032493 rs11646260 16 54001529 rs192014550 1.87066e-05
16 54032493 rs11646260 16 54002172 rs140765996 3.778e-05
16 54032493 rs11646260 16 54002294 16:54002294 5.72312e-05
16 54032493 rs11646260 16 54002356 rs144710532 0.0428216
16 54032493 rs11646260 16 54002845 rs59578934 5.72312e-053-4. Visualizing LD with SNPplotter
So we calculated LDs for all possible combinations of allele pairs. Print out the graph for the computed LD. Install snp.plotter for LD graph printing and execute the following command. This is an example of drawing haplotype SNP sets and LD graph on two racial groups.
Install Xming instead of Xmanager for opensource viewing of server screen display.
Intsall snp.plotter R package and then execute plotting.
[soh1@x020 vcf]$ cd ..
[soh1@x020 RareVariant]$ cd plot
[soh1@x020 plot]$ ls
config.txt d1_hap.txt d1_ss.txt d2_hap.txt d2_ss.txt null_d1_controls.dat null_rsq_phys_color.pdf palette.txt
[soh1@x020 plot]$ R
> library(snp.plotter)
Loading required package: grid
> snp.plotter(config.file="config.txt")
START READ.CONFIG
FINISH READ.CONFIG
START CREATE.COLOR.LIST
FINISH CREATE.COLOR.LIST
START CREATE.SYMBOL.LIST
FINISH CREATE.SYMBOL.LIST
START RETRIEVE.DATA
START SET.IMAGE.PARAMETERS
FINISH SET.IMAGE.PARAMETERS
START FIX.VALUES
FINISH FIX.VALUES
START SET.IMAGE.PARAMETERS
FINISH SET.IMAGE.PARAMETERS
START FIX.VALUES
FINISH FIX.VALUES
START DRAW.PLOT.GRID.SETUP
FINISH DRAW.PLOT.GRID.SETUP
START FIX.VALUES
FINISH FIX.VALUES
START DRAW.PLOT.GRID.SNP.NAMES
FINISH DRAW.PLOT.GRID.SNP.NAMES
START DRAW.PLOT.GRID.SS
FINISH DRAW.PLOT.GRID.SS
START DRAW.PLOT.GRID.HAP
FINISH DRAW.PLOT.GRID.HAP
START FIX.VALUES
FINISH FIX.VALUES
START DRAW.PLOT.GRID.SS
FINISH DRAW.PLOT.GRID.SS
START DRAW.PLOT.GRID.HAP
FINISH DRAW.PLOT.GRID.HAP
FINISH RETRIEVE.DATA
START DRAW.LEGEND
FINISH DRAW.LEGEND
START DRAW.PLOT.LD.PLOT
FINISH DRAW.PLOT.LD.PLOTYou can see that the R library runs on a config file config.txt. It’s got following contents:
[soh1@x020 plot]$ cat config.txt
SNP.FILE=d1_ss.txt,d2_ss.txt
HAP.FILE=d1_hap.txt,d2_hap.txt
PALETTE.FILE=palette.txt
EVEN.SPACED=FALSE
USE.GBL.PVAL=TRUE
DISP.HAP=TRUE
DISP.LDMAP=TRUE
LD.COLOR.SCHEME=heat
COLOR.LIST=red,blue
SYMBOLS=circle-fill,square-fill
PVAL.THRESHOLD=1
LAB.Y=log
GENOTYPE.FILE=null_d1_controls.dat
LD.TYPE=rsquare
DISP.COLOR.BAR=TRUE
DISP.TYPE=symbol
DISP.LEGEND=TRUE
SAMPLE.LABELS=Pop.1,Pop.2
IMAGE.TYPE=pdf
DISP.SNP=TRUE
DISP.MULT.LAB.X=FALSE
IMAGE.TITLE=" "
IMAGE.NAME=null_rsq_phys_color
IMAGE.SIZE=3.5
CONNECTING.LINES.FACTOR=1.5
DISP.PHYS.DIST=TRUE
CONNECTING.LINES.ADJ=0.02SNP.FILE: tab-delimited text file that’s got p-values of single SNPs. It’s got columns of SNP.NAME, LOC, SS.PVAL. ASSOC shows whether it is a allele for disease risk or prevention. SNP.NAME shows the name of that SNP, LOC means locus, SS.PVAL means p-value of that particular SNP. Examples are like the following:
[soh1@x020 plot]$ less d1_ss.txtASSOC SNP.NAME LOC SS.PVAL
+ rs0000001 50017600 0.0082
+ rs0000002 50056889 0.0101
+ rs0000003 50343044 0.00754
+ rs0000004 50373804 0.0391
+ rs0000005 50375238 2.58E-05
+ rs0000006 50492148 0.0128
+ rs0000007 50522339 0.0504
+ rs0000008 50542551 0.222
+ rs0000009 50623862 0.00269
+ rs00000010 50646467 0.0695
+ rs00000011 50658231 0.341
+ rs00000012 50664029 0.0114
+ rs00000013 50677804 0.000548
+ rs00000014 50715691 0.00111
+ rs00000015 50746424 0.131
+ rs00000016 50766173 0.829
+ rs00000017 51127051 0.926
+ rs00000018 51273874 0.548
+ rs00000019 51348270 0.641
+ rs00000020 51375954 0.817
d1_ss.txt (END)[soh1@x020 plot]$ less d1_hap.txtHAP.FILE: tab-delimited file that has haplotype p-value, AAOC, G.PVAL, I.PVAL. G.PVAL shows global p-value of each haplotype, I.PVAL shows individual p-value.
LD.TYPE: For LD measurement there are two options: dprime or rsquare. dprime and rsquare
All the other options can be properly controlled with Display option. LD graph resulting from the example files are as follows (null_rsq_phys_color.pdf)
IMAGE.NAME=null_rsq_phys_color option in configuration file.
[soh1@x020 plot]$ okular null_rsq_phys_color.pdf
So, to explain this data, note that the above exercise is taken from an article on bioinformatics: “snp.plotter: an R-based SNP/haplotype association and linkage disequilibrium plotting package”. The HapMap project catalogs SNPs from populations with African, Asian and European ancestry (The International HapMap Consortium, 2005). Sample data for 20 SNPs was obtained from HapMap and two case-control populations with 500 cases and 500 controls were simulated using the Simulation of Haplotype Heterogeneity, Interaction and Population Stratification (SH2IPS) R package.
If the SNPs have same p-values, that is interpreted as there’s a linkage disequilibrium and the loci are associated with each other.
Dotted lines represent P-value thresholds.
4. HLA alternative alleles, HLA SNPs and Imputation of Amino Acid Polymorphisms in HLA
HLA gene is an important gene that dictates the graft (organ transplantation) success rate, and it has been identified as one of the largest risk factor in autoimmune diseases in multiple GWAS studies.
However, it shows a wide spectrum of polymorphisms and genotype determination is difficult, so is still remaining as one of bioinformatics’s biggest challenges.
Most of the current standard NGS technologies do not guarantee sequencing results of HLA regions. Therefore, if we can imputate the insufficient information and estimate which genes among the HLA genes and which variants are associated with a particular disease, then it would greatly help looking for disease antigens and excavating disease target genes.
There have been quite a number of algorithms suggested, but SNP2HLA (Imputation of Amino Acid Polymorphisms in Human Leukocyte Antigens) that was published in 2014 was distinguishable from other algorithms in that it utilized the intergenic SNPs that exist between HLA genes and comparing that to the reference sequence to imputate the missing HLA genotype information. So now we dive into SNPs of HLA genes and amino acid polymorphism imputation.
Now, we gotta use the .csh1 file. the file snp2hla.csh contains dependency information as follows:
It says that you’re required to download the binary executables and place the files in the same folder as the script. And these are the softwares we need:
- PLINK (1.07)
- Beagle (3.0.4)
merge_tables.pl(Perl script to merge files indexed by a specific column)linkage2beagleandbeagle2linkage(Beagle utilities to PED <-> Beagle format)- ParseDosage.csh (Converts Beagle posterior probabilities [.gprobs] to dosages in PLINK format [.dosage])
Also, we need two inputs:
- Plink dataset
- Reference dataset (beagle format)
If you open snp2hla.csh through vim and go to the line with checking dependencies code chunk, it looks like this:
[soh1@x020 RareVariant]$ cd snp2hla/
[soh1@x020 snp2hla]$ vi SNP2HLA.csh# CHECK FOR DEPENDENCIES
if (! -e `which $4`) then
echo "Please install PLINK (http://pngu.mgh.harvard.edu/~purcell/plink/download.shtm
echo "tcsh: use plink"
echo "bash: use ./plink"
exit 1
else if (! -e $SCRIPTPATH/beagle.jar) then
else if (! -e $SCRIPTPATH/linkage2beagle.jar) then
echo "Please copy linkage2beagle.jar included in the beagle 3.0.4 zip file (beagle.3
else if (! -e $SCRIPTPATH/beagle2linkage.jar) then # We use beagle2linkage (Buhm, 8/13/1
echo "Please copy beagle2linkage.jar (http://faculty.washington.edu/browning/beagle_
else if (! -e $MERGE) then
echo "Please copy merge_tables.pl (included with this package) into $SCRIPTPATH/"; e
else if (! -e $PARSEDOSAGE) then
echo "Please copy ParseDosage.csh (included with this package) into $SCRIPTPATH/"; e
endifIf we look into the directory,
[soh1@x020 snp2hla]$ ls
1958BC.bed HM_CEU_REF.bed HM_CEU_REF.FRQ.log ParseDosage.csh
1958BC.bim HM_CEU_REF.bgl.phased HM_CEU_REF.log README.txt
1958BC.fam HM_CEU_REF.bim HM_CEU_REF.markers SNP2HLA.csh
beagle2linkage.jar HM_CEU_REF.fam linkage2beagle.jar
beagle.jar HM_CEU_REF.FRQ.frq merge_tables.plwe can see that we already have 3. merge_tables.pl, 4. linkage2beagle, beagle2linkage, and 2. beagle. We’re missing plink only.
So I downloaded plink-1.07-x86_64.zip from http://zzz.bwh.harvard.edu/plink/index.shtml
The usage goes like this:
# USAGE: ./SNP2HLA.csh DATA (.bed/.bim/.fam) REFERENCE (.bgl.phased/.markers) OUTPUT pl
ink {optional: max_memory[mb] window_size}Exercise data consists of 10 British people born in 1958 (1958BC) and CEU (HM_CEU_REF: Utah residents with ancestry from Northern and Western Europe) from 1KGP as reference sequence. The input file, 1958BC has been made into .bed/.bim/.fam file to coordinate with PLINK input format. The reference seq HM_CEU_REF data are .bgl.phased/.markers files fitted for PLINK input format as well. The default setting for executing SNP2HLA is JAVA memory 2GB, marker window size 1000, so no further modification is required.
Now we execute imputation of 10 people’s sample (1958BC.bed, 1958BC.bim, 1958BC.fam) accompanied by CEU reference data (HM_CEU_REF.bgl.phased/HM_CEU_REF.markers).
[soh1@x020 snp2hla]$ ./SNP2HLA.csh 1958BC HM_CEU_REF 1958BC_IMPUTED plink 2000 1000
-bash: ./SNP2HLA.csh: Permission deniedExecuting resulted in a ‘Permission denied’ error.
[soh1@x020 snp2hla]$ chmod 777 SNP2HLA.csh # Change permission of SNP2HLA.csh
[soh1@x020 snp2hla]$ cd plink-1.07-x86_64/
[soh1@x020 plink-1.07-x86_64]$ mv * .. # Move all plink files to above directory
[soh1@x020 plink-1.07-x86_64]$ cd ..
[soh1@x020 snp2hla]$ chmod 777 * # Change permission of all files contained in the directorySince there was an error by the script in finding where plink was located, I designated it with ./plink, instead of plink as indicated by the textbook.
[soh1@x020 snp2hla]$ ./SNP2HLA.csh 1958BC HM_CEU_REF 1958BC_IMPUTED ./plink 2000 1000
SNP2HLA: Performing HLA imputation for dataset 1958BC
- Java memory = 2000Mb
- Beagle window size = 1000 markers
[1] Extracting SNPs from the MHC.
[2] Performing SNP quality control.
[3] Convering data to beagle format.
[4] Performing HLA imputation (see 1958BC_IMPUTED.bgl.log for progress).
[5] Converting posterior probabilities to PLINK dosage format.
[6] Converting imputation genotypes to PLINK .ped format.
DONE!Now check out the file list and see what’s become different.
Previous
[soh1@x020 snp2hla]$ ls
1958BC.bed HM_CEU_REF.bed HM_CEU_REF.FRQ.log ParseDosage.csh
1958BC.bim HM_CEU_REF.bgl.phased HM_CEU_REF.log README.txt
1958BC.fam HM_CEU_REF.bim HM_CEU_REF.markers SNP2HLA.csh
beagle2linkage.jar HM_CEU_REF.fam linkage2beagle.jar
beagle.jar HM_CEU_REF.FRQ.frq merge_tables.plAfter
[soh1@x020 snp2hla]$ ls
1958BC.bed beagle2linkage.jar HM_CEU_REF.markers
1958BC.bim beagle.jar linkage2beagle.jar
1958BC.fam COPYING.txt merge_tables.pl
1958BC_IMPUTED.bed gPLINK.jar ParseDosage.csh
1958BC_IMPUTED.bgl.gprobs HM_CEU_REF.bed plink
1958BC_IMPUTED.bgl.log HM_CEU_REF.bgl.phased plink-1.07-x86_64
1958BC_IMPUTED.bgl.phased HM_CEU_REF.bim README.txt
1958BC_IMPUTED.bgl.r2 HM_CEU_REF.fam SNP2HLA.csh
1958BC_IMPUTED.bim HM_CEU_REF.FRQ.frq test.map
1958BC_IMPUTED.dosage HM_CEU_REF.FRQ.log test.ped
1958BC_IMPUTED.fam HM_CEU_REF.logPicture of after. 
Now there are the imputed files. So far, these files have been generated:
1958BC_IMPUTED.bed: PLINK format genotype info binary file after imputation is performed.1958BC_IMPUTED.bim: Identifier file after imputation, which contains chr, IDs, genomic distances (morgans), base pair position, and allele type infos.1958BC_IMPUTED.fam: 10 people sample after imputation in PLINK format file. Contains Family ID, Individual ID, Paternal ID, Maternal ID, Sex(1=male, 2=female, other=unknown), Phenotype(1=unaffected, 2=affected, 0=miss, -9=missing)1958BC_IMPUTED.dosage: Imputation weighted weight to find the highest statistical value peak for all identifiers (HLA alleles, amino acid, SNP). Dosage file is a Beagle format, the row has identifiers and column has identifier info and individual imputations.1958BC_IMPUTED.bgl.phased: Imputation posterior probability for all identifiers (HLA allele, amino acid, SNP)1958BC IMPUTED.bgl.gprobs
If you open the imputed files (1958_IMPUTED.bim, 1958_IMPUTED.fam, 1958_IMPUTED.dosage),
[soh1@x020 snp2hla]$ head 1958BC_IMPUTED.bim
6 rs13207673 0 26009112 G A
6 rs9356991 0 26009737 T G
6 rs6910174 0 26012393 A G
6 rs3846838 0 26019754 G A
6 rs6905887 0 26020082 G A
6 rs3799369 0 26020613 C T
6 rs6932113 0 26021077 A G
6 rs6938233 0 26022056 A G
6 rs2071299 0 26022780 T C
6 rs2071298 0 26022880 A G
[soh1@x020 snp2hla]$ head 1958BC_IMPUTED.fam
WTCCC66758 WTCCC66758 0 0 2 1
WTCCC66061 WTCCC66061 0 0 1 1
WTCCC66073 WTCCC66073 0 0 1 1
WTCCC66085 WTCCC66085 0 0 1 1
WTCCC66097 WTCCC66097 0 0 1 1
WTCCC66109 WTCCC66109 0 0 1 1
WTCCC66121 WTCCC66121 0 0 1 1
WTCCC66133 WTCCC66133 0 0 1 1
WTCCC66145 WTCCC66145 0 0 1 1
WTCCC66062 WTCCC66062 0 0 1 1
[soh1@x020 snp2hla]$ head 1958BC_IMPUTED.dosage
rs13207673 A G 1.047 1.027 1.064 1.018 0.931 0.982 1.230 1.030 1.016 1.157
rs9356991 T G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs6910174 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs3846838 G A 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs6905887 G A 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs3799369 C T 1.110 1.096 1.128 1.098 1.025 1.062 0.885 1.112 1.103 1.014
rs6932113 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs6938233 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs2071299 T C 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs2071298 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
they look like this.
SH has its own features, BASH has incorporated the features of other shells including that of CSH with its own features which provides it with more features and makes it the most widely used command processor. 3.CSH was developed by Bill Joy in the late 1970s while BASH was developed by Brian Fox. Read more: Difference Between CSH and BASH | Difference Between http://www.differencebetween.net/technology/software-technology/difference-between-csh-and-bash/#ixzz6WOg9HJNI] file. the file snp2hla.csh contains dependency information as follows:
It says that you’re required to download the binary executables and place the files in the same folder as the script. And these are the softwares we need:
- PLINK (1.07)
- Beagle (3.0.4)
merge_tables.pl(Perl script to merge files indexed by a specific column)linkage2beagleandbeagle2linkage(Beagle utilities to PED <-> Beagle format)- ParseDosage.csh (Converts Beagle posterior probabilities [.gprobs] to dosages in PLINK format [.dosage])
Also, we need two inputs:
- Plink dataset
- Reference dataset (beagle format)
If you open snp2hla.csh through vim and go to the line with checking dependencies code chunk, it looks like this:
[soh1@x020 RareVariant]$ cd snp2hla/
[soh1@x020 snp2hla]$ vi SNP2HLA.csh# CHECK FOR DEPENDENCIES
if (! -e `which $4`) then
echo "Please install PLINK (http://pngu.mgh.harvard.edu/~purcell/plink/download.shtm
echo "tcsh: use plink"
echo "bash: use ./plink"
exit 1
else if (! -e $SCRIPTPATH/beagle.jar) then
else if (! -e $SCRIPTPATH/linkage2beagle.jar) then
echo "Please copy linkage2beagle.jar included in the beagle 3.0.4 zip file (beagle.3
else if (! -e $SCRIPTPATH/beagle2linkage.jar) then # We use beagle2linkage (Buhm, 8/13/1
echo "Please copy beagle2linkage.jar (http://faculty.washington.edu/browning/beagle_
else if (! -e $MERGE) then
echo "Please copy merge_tables.pl (included with this package) into $SCRIPTPATH/"; e
else if (! -e $PARSEDOSAGE) then
echo "Please copy ParseDosage.csh (included with this package) into $SCRIPTPATH/"; e
endifIf we look into the directory,
[soh1@x020 snp2hla]$ ls
1958BC.bed HM_CEU_REF.bed HM_CEU_REF.FRQ.log ParseDosage.csh
1958BC.bim HM_CEU_REF.bgl.phased HM_CEU_REF.log README.txt
1958BC.fam HM_CEU_REF.bim HM_CEU_REF.markers SNP2HLA.csh
beagle2linkage.jar HM_CEU_REF.fam linkage2beagle.jar
beagle.jar HM_CEU_REF.FRQ.frq merge_tables.plwe can see that we already have 3. merge_tables.pl, 4. linkage2beagle, beagle2linkage, and 2. beagle. We’re missing plink only.
So I downloaded plink-1.07-x86_64.zip from http://zzz.bwh.harvard.edu/plink/index.shtml
The usage goes like this:
# USAGE: ./SNP2HLA.csh DATA (.bed/.bim/.fam) REFERENCE (.bgl.phased/.markers) OUTPUT pl
ink {optional: max_memory[mb] window_size}Exercise data consists of 10 British people born in 1958 (1958BC) and CEU (HM_CEU_REF: Utah residents with ancestry from Northern and Western Europe) from 1KGP as reference sequence. The input file, 1958BC has been made into .bed/.bim/.fam file to coordinate with PLINK input format. The reference seq HM_CEU_REF data are .bgl.phased/.markers files fitted for PLINK input format as well. The default setting for executing SNP2HLA is JAVA memory 2GB, marker window size 1000, so no further modification is required.
Now we execute imputation of 10 people’s sample (1958BC.bed, 1958BC.bim, 1958BC.fam) accompanied by CEU reference data (HM_CEU_REF.bgl.phased/HM_CEU_REF.markers).
[soh1@x020 snp2hla]$ ./SNP2HLA.csh 1958BC HM_CEU_REF 1958BC_IMPUTED plink 2000 1000
-bash: ./SNP2HLA.csh: Permission deniedExecuting resulted in a ‘Permission denied’ error.
[soh1@x020 snp2hla]$ chmod 777 SNP2HLA.csh # Change permission of SNP2HLA.csh
[soh1@x020 snp2hla]$ cd plink-1.07-x86_64/
[soh1@x020 plink-1.07-x86_64]$ mv * .. # Move all plink files to above directory
[soh1@x020 plink-1.07-x86_64]$ cd ..
[soh1@x020 snp2hla]$ chmod 777 * # Change permission of all files contained in the directorySince there was an error by the script in finding where plink was located, I designated it with ./plink, instead of plink as indicated by the textbook.
[soh1@x020 snp2hla]$ ./SNP2HLA.csh 1958BC HM_CEU_REF 1958BC_IMPUTED ./plink 2000 1000
SNP2HLA: Performing HLA imputation for dataset 1958BC
- Java memory = 2000Mb
- Beagle window size = 1000 markers
[1] Extracting SNPs from the MHC.
[2] Performing SNP quality control.
[3] Convering data to beagle format.
[4] Performing HLA imputation (see 1958BC_IMPUTED.bgl.log for progress).
[5] Converting posterior probabilities to PLINK dosage format.
[6] Converting imputation genotypes to PLINK .ped format.
DONE!Now check out the file list and see what’s become different.
Previous
[soh1@x020 snp2hla]$ ls
1958BC.bed HM_CEU_REF.bed HM_CEU_REF.FRQ.log ParseDosage.csh
1958BC.bim HM_CEU_REF.bgl.phased HM_CEU_REF.log README.txt
1958BC.fam HM_CEU_REF.bim HM_CEU_REF.markers SNP2HLA.csh
beagle2linkage.jar HM_CEU_REF.fam linkage2beagle.jar
beagle.jar HM_CEU_REF.FRQ.frq merge_tables.plAfter
[soh1@x020 snp2hla]$ ls
1958BC.bed beagle2linkage.jar HM_CEU_REF.markers
1958BC.bim beagle.jar linkage2beagle.jar
1958BC.fam COPYING.txt merge_tables.pl
1958BC_IMPUTED.bed gPLINK.jar ParseDosage.csh
1958BC_IMPUTED.bgl.gprobs HM_CEU_REF.bed plink
1958BC_IMPUTED.bgl.log HM_CEU_REF.bgl.phased plink-1.07-x86_64
1958BC_IMPUTED.bgl.phased HM_CEU_REF.bim README.txt
1958BC_IMPUTED.bgl.r2 HM_CEU_REF.fam SNP2HLA.csh
1958BC_IMPUTED.bim HM_CEU_REF.FRQ.frq test.map
1958BC_IMPUTED.dosage HM_CEU_REF.FRQ.log test.ped
1958BC_IMPUTED.fam HM_CEU_REF.logPicture of after.
Now there are the imputed files. So far, these files have been generated:
1958BC_IMPUTED.bed: PLINK format genotype info binary file after imputation is performed.1958BC_IMPUTED.bim: Identifier file after imputation, which contains chr, IDs, genomic distances (morgans), base pair position, and allele type infos.1958BC_IMPUTED.fam: 10 people sample after imputation in PLINK format file. Contains Family ID, Individual ID, Paternal ID, Maternal ID, Sex(1=male, 2=female, other=unknown), Phenotype(1=unaffected, 2=affected, 0=miss, -9=missing)1958BC_IMPUTED.dosage: Imputation weighted weight to find the highest statistical value peak for all identifiers (HLA alleles, amino acid, SNP). Dosage file is a Beagle format, the row has identifiers and column has identifier info and individual imputations.1958BC_IMPUTED.bgl.phased: Imputated genotype file. It’s in Beagle format, the row corresponds to identifier and two columns correspond to one individual’s sample.1958BC_IMPUTED.bgl.gprobs: Imputation posterior probability for all identifiers (HLA allele, amino acid, SNP)1958BC_IMPUTED.bgl.r2: The correlation coefficient (\(r^2\)) of imputation calculated by genotype.
If you open the imputed files (1958_IMPUTED.bim, 1958_IMPUTED.fam, 1958_IMPUTED.dosage),
[soh1@x020 snp2hla]$ head 1958BC_IMPUTED.bim
6 rs13207673 0 26009112 G A
6 rs9356991 0 26009737 T G
6 rs6910174 0 26012393 A G
6 rs3846838 0 26019754 G A
6 rs6905887 0 26020082 G A
6 rs3799369 0 26020613 C T
6 rs6932113 0 26021077 A G
6 rs6938233 0 26022056 A G
6 rs2071299 0 26022780 T C
6 rs2071298 0 26022880 A G
[soh1@x020 snp2hla]$ head 1958BC_IMPUTED.fam
WTCCC66758 WTCCC66758 0 0 2 1
WTCCC66061 WTCCC66061 0 0 1 1
WTCCC66073 WTCCC66073 0 0 1 1
WTCCC66085 WTCCC66085 0 0 1 1
WTCCC66097 WTCCC66097 0 0 1 1
WTCCC66109 WTCCC66109 0 0 1 1
WTCCC66121 WTCCC66121 0 0 1 1
WTCCC66133 WTCCC66133 0 0 1 1
WTCCC66145 WTCCC66145 0 0 1 1
WTCCC66062 WTCCC66062 0 0 1 1
[soh1@x020 snp2hla]$ head 1958BC_IMPUTED.dosage
rs13207673 A G 1.047 1.027 1.064 1.018 0.931 0.982 1.230 1.030 1.016 1.157
rs9356991 T G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs6910174 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs3846838 G A 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs6905887 G A 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs3799369 C T 1.110 1.096 1.128 1.098 1.025 1.062 0.885 1.112 1.103 1.014
rs6932113 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs6938233 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs2071299 T C 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
rs2071298 A G 1.476 1.440 1.478 1.453 1.410 1.416 1.153 1.459 1.450 1.317
they look like this.
As stated above, GWAS have not been effective in querying variation within HLA genes. Probe-based methods for HLA genotyping have been limited in resolution because of the highly polymorphic nature of these genes. Therefore, strategies for direct HLA allele typing have come forward, including sequence specific oligonucleotide (SSO) hybridization, capillary (Sanger) sequencing, and NGS. Unfortunately these approaches are not easily scalable for large cohorts because they are labor-intensive, tedious, time-consuming, and expensive. Jia’s group devised a simple approach using selected tag SNPs that are in strong LD with classical HLA alleles. Subsequently more sophisticated approaches that model LD patterns of surrounding SNPs have been developed to imputed classical HLA alleles.
The reference panels were constructed based on genotyping data collected in individuals of European ancestry with the HapMap-CEPH panel that contains 3,924 SNPs (genotyped with Illumina GoldenGate) and 4-digit classical HLA types for HLA-A, -B, -C, -DQA1, -DQB1 and -DRB1 for 90 unrelated iundividuals (180 haplotypes). Also, the Type 1 Diabetes Genetics Consortium (T1DGC) panel contains 5,868 SNPs (genotyped with Illumina Immunochip) and 4-digit classical HLA types for HLA-A, -B, -C, -DPA1, -DPB1, -DQA1, -DQB1 and -DRB1 for 5,225 unrelated individuals (10,450 haplotypes). The T1DGC panel contains more unique HLA alleles and amino acid polymorphisms becasue of its significantly larger sample size.
So, I couldn’t understand the concept of dosage in imputation. Dosage is a simple linear transformation of the posterior genotype probabilities usually coming from imputation. The concept’s example is demonstrated in the following Biostars thread: what does it mean when the genotype for SNP1 for Patient A = 1.999 and genotype for SNP1 for Patient B = 1.865.
These values are dosages and they are calculated like this:
Genotype probabilities - A/A: 0.1 - A/B: 0.4 - B/B: 0.5
- A/A score = 0 - A/B score = 1 - B/B score = 2
\(0.1*0 + 0.4*1 + 0.5*2 = 1.4\)
The dosage is 1.4
For example above this, where patient A shows dosage of 1.999 and patient B shows dosage of 1.865 for the certain SNP1, this can be interpreted as both patients A and B have SNP of 2 at the locus for SNP1, but patient A is more likely to have a 2 there compared to patient B.
Now, let’s move on to association study in PLINK with the imputed dosage file, as we have previously done before.
The following is association study usage in PLINK:
plink --noweb -- dosage OUTPUT.dosage noheader format=1 --fam OUTPUT.fam --logistic --out OUTPUT.assoc--nowebmeans that we’re not gonna connect to internet and run this procedure locally--dosage OUTPUT.dosagegenerates OUTPUT.dosage file.noheaderoption to be used when there’s no header in the OUTPUT.dosage format = N: Dosage, two probabilities or three (N=1,2,3)--fam OUTPUT.famgenerates OUTPUT.fam file--logisticdo a logistic regression analysis--out OUTPUT.assocgenerates the output result file of the whole association test, OUTPUT.assoc.
[soh1@x020 snp2hla]$ ./plink --noweb --dosage 1958BC_IMPUTED.dosage noheader format=1 --fam 1958BC_IMPUTED.fam --logistic --out 1958BC_IMPUTED
@----------------------------------------------------------@
| PLINK! | v1.07 | 10/Aug/2009 |
|----------------------------------------------------------|
| (C) 2009 Shaun Purcell, GNU General Public License, v2 |
|----------------------------------------------------------|
| For documentation, citation & bug-report instructions: |
| http://pngu.mgh.harvard.edu/purcell/plink/ |
@----------------------------------------------------------@
Skipping web check... [ --noweb ]
Writing this text to log file [ 1958BC_IMPUTED.log ]
Analysis started: Sun Aug 30 18:14:22 2020
Options in effect:
--noweb
--dosage 1958BC_IMPUTED.dosage
noheader
format=1
--fam 1958BC_IMPUTED.fam
--logistic
--out 1958BC_IMPUTED
Reading pedigree information from [ 1958BC_IMPUTED.fam ]
10 individuals read from [ 1958BC_IMPUTED.fam ]
10 individuals with nonmissing phenotypes
Assuming a disease phenotype (1=unaff, 2=aff, 0=miss)
Missing phenotype value is also -9
0 cases, 10 controls and 0 missing
9 males, 1 females, and 0 of unspecified sex
Reading dosage information from [ 1958BC_IMPUTED.dosage ]
Format set to one dosage per genotype
Writing results to [ 1958BC_IMPUTED.assoc.dosage ]
Processed 6700 markers
Analysis finished: Sun Aug 30 18:14:22 2020[soh1@x020 snp2hla]$ ll | grep '8월 30'
-rw-rw-r-- 1 soh1 soh1 436610 8월 30 17:52 1958BC_IMPUTED.assoc.dosage
-rw-rw-r-- 1 soh1 soh1 1279 8월 30 17:52 1958BC_IMPUTED.log
-rw-rw-r-- 1 soh1 soh1 555 8월 30 17:50 plink.logSo if you look into the generated files, you can see that assoc.dosage file and log file have been created. 1958BC_IMPUTED.assoc.dosage file contains SNP ID SNP, A1 (analyzed allele genotype), A2 (reference allele genotype),FRQ frequency, INFO R-squared quality metric/information content, OR oddds ratio, SE Standard error of effect (not odds ratio) estimate, P association test p-value. Further information on PLINK file formats are described in this page. Search for .assoc.dosage. The file content looks like this:
[soh1@x020 snp2hla]$ more 1958BC_IMPUTED.assoc.dosage
SNP A1 A2 FRQ INFO OR SE P
rs13207673 A G 0.5251 0.0132 NA NA NA
rs9356991 T G 0.7026 0.0216 NA NA NA
rs6910174 A G 0.7026 0.0216 NA NA NA
rs3846838 G A 0.7026 0.0216 NA NA NA
rs6905887 G A 0.7026 0.0216 NA NA NA
rs3799369 C T 0.5317 0.0097 NA NA NA
rs6932113 A G 0.7026 0.0216 NA NA NA
rs6938233 A G 0.7026 0.0216 NA NA NA
rs2071299 T C 0.7026 0.0216 NA NA NA
rs2071298 A G 0.7026 0.0216 NA NA NA
rs7450342 C T 0.7575 0.0042 NA NA NA
rs1540273 G A 0.7025 0.0217 NA NA NA
rs7770139 C T 0.7026 0.0216 NA NA NA
rs9295676 A C 0.5135 0.0072 NA NA NA
rs6940007 C A 0.5251 0.0131 NA NA NA
rs2328903 G A 0.7083 0.0226 NA NA NA
rs9358896 A C 0.7041 0.0222 NA NA NA
rs7746105 G T 0.5551 0.0114 NA NA NA
rs2051541 T C 0.7105 0.0169 NA NA NA
rs1436306 C T 0.7075 0.0226 NA NA NA
rs199730 C T 0.5573 0.0116 NA NA NA
rs199729 T C 0.5573 0.0116 NA NA NA
rs6929805 T A 0.7076 0.0227 NA NA NA
rs1115920 G A 0.7069 0.0238 NA NA NA
rs11758372 T C 0.5547 0.0123 NA NA NA
rs1436310 G C 0.7186 0.0253 NA NA NA
rs6906460 A T 0.5302 0.0112 NA NA NA
rs199755 C T 0.6264 0.0105 NA NA NA
rs7766267 G C 0.5502 0.0117 NA NA NA
rs2051538 A G 0.5321 0.0114 NA NA NA
rs6901039 A C 0.6281 0.0104 NA NA NA
rs9467658 G T 0.7179 0.0256 NA NA NA
rs199752 C T 0.6306 0.0104 NA NA NA
rs9379818 T G 0.7111 0.0251 NA NA NA
rs2032449 G C 0.7069 0.0246 NA NA NA
rs3752420 T C 0.7086 0.0248 NA NA NA
rs3752419 A G 0.7071 0.0249 NA NA NA
rs10484433 A C 0.5218 0.0145 NA NA NA
rs10484435 C A 0.5194 0.0137 NA NA NA
rs2230655 G A 0.6346 0.0114 NA NA NA
rs3752418 C G 0.5278 0.0106 NA NA NA
rs6922788 G A 0.6426 0.0122 NA NA NA
rs8384 G C 0.5843 0.0158 NA NA NA
--More--(0%)
Now, in this dosage association analysis report, look for rs211453.
rs211453’s Tested allele (sample) is C, Major allele (reference) is A. It’s got frequency of 0.3000 and information content is 0.5714, the odds ratio is 1, and standard error is 15736.1048, p-value is 1.
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